Finite Group Databasebeta

← C3×#25525 #10644132

Subgroups — C3×#25525 #10644132

Order 768.

1072 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3495C211yesmaximal, characteristic
2C3×#3095C211yesmaximal, characteristic, complemented
3C3×#3056C211yesmaximal, characteristic
4C3×#2857C211yesmaximal, characteristic, complemented
5C3×#2060C211yesmaximal, characteristic, complemented
6C3×#2038C211yesmaximal, characteristic, complemented
7C3×#2028C211yesmaximal, characteristic, complemented
8C3×#2005C211yesmaximal, characteristic, complemented
9C3×#1901C211yesmaximal, characteristic, complemented
10C3×#1896C211yesmaximal, characteristic
11C3×#1886C211yesmaximal, characteristic, complemented
12C3×#1882C211yesmaximal, characteristic, complemented
13C3×#1859C211yesmaximal, characteristic, complemented
14C3×#1857C211yesmaximal, characteristic, complemented
15C2×C3×#339C211yesmaximal, characteristic, complemented
16#25525C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#137C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C3×#556—21no—
20C3×#554—21no—
21C3×#552—21no—
22C3×#552—22no—
23C3×#552—21no—
24C3×#551—22no—
25C3×#544C2211yescharacteristic
26C3×#542—21no—
27C3×#541—21no—
28C3×#536C2211yescharacteristic
29C3×#533—21no—
30C2×C3×C4⋊Q8C2211yescharacteristic
31C3×#529—21no—
32C3×#525C2211yescharacteristic
33C2×C3×C22⋊Q8C2211yescharacteristic
34C2×C3×C22⋊Q8C2211yescharacteristic
35C3×#520C2211yescharacteristic
36C3×#519C2211yescharacteristic
37C2×C3×#117C2211yescharacteristic
38C22×C3×C42C2211yescharacteristic
39C3×#485—21no—
40C3×#485—21no—
41C3×#484—21no—
42C3×#483—21no—
43C3×#470—21no—
44C3×#468—21no—
45C3×#467—21no—
46C3×#465—21no—
47C3×#428C2211yescharacteristic
48C3×#428C2211yescharacteristic
49C3×#428C2211yescharacteristic
50C2×C3×#104C2211yescharacteristic
51C2×C3×#104C2211yescharacteristic
52C3×#419C2211yescharacteristic
53C3×#419C2211yescharacteristic
54C3×#419C2211yescharacteristic
55C3×#417C2211yescharacteristic
56C2×C3×#101C2211yescharacteristic
57C2×C3×#101C2211yescharacteristic
58C3×#407C2211yescharacteristic
59C3×#391C2211yescharacteristic
60C3×#391C2211yescharacteristic
61C3×#389—22no—
62C3×#384C2211yescharacteristic
63C3×#380—22no—
64C3×#343C2211yescharacteristic
65C3×#343C2211yescharacteristic
66C3×#339C2211yescharacteristic
67C3×#339C2211yescharacteristic
68C3×#339C2211yescharacteristic
69C3×#339C2211yescharacteristic
70C3×#339C2211yescharacteristic
71C3×#339C2211yescharacteristic
72#3495C2×C311yescharacteristic
73#3095C2×C311yescharacteristic, complemented
74#3056C2×C311yescharacteristic
75#2857C2×C311yescharacteristic, complemented
76#2060C2×C311yescharacteristic, complemented
77#2038C2×C311yescharacteristic, complemented
78#2028C2×C311yescharacteristic, complemented
79#2005C2×C311yescharacteristic, complemented
80#1901C2×C311yescharacteristic, complemented
81#1896C2×C311yescharacteristic
82#1886C2×C311yescharacteristic, complemented
83#1882C2×C311yescharacteristic, complemented
84#1859C2×C311yescharacteristic, complemented
85#1857C2×C311yescharacteristic, complemented
86C2×#339C2×C311yescharacteristic, complemented
87C2×C3×#41C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C22×C3×Q8C2311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C3×#137—22no—
93C3×#137—41no—
94C2×C3×Q16—21no—
95C2×C3×SD16—21no—
96C2×C3×M16—21no—
97C2×C3×M16—22no—
98C2×C3×M16—41no—
99C2×C3×M16C2311yescharacteristic
100C2×C3×M16C2311yescharacteristic
101C2×C3×M16C2311yescharacteristic
102C2×C3×M16C2311yescharacteristic
103C22×C3×C8—21no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—21no—
106C3×C4⋊Q8—21no—
107C3×C4⋊Q8—22no—
108C3×C4⋊Q8—41no—
109C3×#126—22no—
110C3×#126—22no—
111C3×#126—22no—
112C3×#126—22no—
113C3×#125—22no—
114C3×#125—22no—
115C3×#125—22no—
116C3×#125—21no—
117C3×#125—21no—
118C3×#124—22no—
119C3×#124—21no—
120C3×#123—22no—
121C3×#123—22no—
122C3×#123—21no—
123C3×#123—22no—
124C3×C22⋊Q8—22no—
125C3×C22⋊Q8—22no—
126C3×C22⋊Q8—21no—
127C3×C22⋊Q8—21no—
128C3×C22⋊Q8—21no—
129C3×C22⋊Q8—21no—
130C3×C22⋊Q8—22no—
131C3×C22⋊Q8—21no—
132C3×C22⋊Q8—21no—
133C3×C22⋊Q8—21no—
134C3×C22⋊Q8—21no—
135C3×C22⋊Q8—21no—
136C3×C22⋊Q8—21no—
137C3×C22⋊Q8D411yescharacteristic
138C3×C22⋊Q8D411yescharacteristic
139C3×#121D411yescharacteristic
140C3×#121D411yescharacteristic
141C3×#120—21no—
142C3×C4×Q8—22no—
143C3×C4×Q8—21no—
144C3×C4×Q8—21no—
145C3×C4×Q8—21no—
146C3×C4×Q8—21no—
147C3×C4×Q8—21no—
148C3×C4×D4—22no—
149C3×C4×D4—21no—
150C3×C4×D4—22no—
151C3×C4×D4—21no—
152C3×C4×D4—21no—
153C3×#117—22no—
154C3×#117—22no—
155C3×#117—21no—
156C3×#117—21no—
157C3×#117—22no—
158C3×#117—21no—
159C3×#117D411yescharacteristic
160C3×#117D411yescharacteristic
161C3×#117C2311yescharacteristic
162C3×#117C2311yescharacteristic
163C3×#117C2311yescharacteristic
164C2×C3×C4⋊C4—21no—
165C2×C3×C4⋊C4—22no—
166C2×C3×C4⋊C4—22no—
167C2×C3×C4⋊C4—21no—
168C2×C3×C4⋊C4D412yes—
169C2×C3×C4⋊C4D411yescharacteristic
170C2×C3×C4⋊C4D411yescharacteristic
171C2×C3×C4⋊C4C2311yescharacteristic
172C2×C3×C4⋊C4C2311yescharacteristic
173C2×C3×C22⋊C4—21no—
174C2×C3×C22⋊C4—21no—
175C2×C3×C22⋊C4D412yes—
176C2×C3×C42—21no—
177C2×C3×C42—22no—
178C2×C3×C42—21no—
179C2×C3×C42—41no—
180C2×C3×C42C2311yescharacteristic
181C2×C3×C42C2311yescharacteristic
182C3×#107—21no—
183C3×#107—21no—
184C3×#107—21no—
185C3×#106—21no—
186C3×#106—21no—
187C3×#106—21no—
188C3×#104—22no—
189C3×#104—41no—
190C3×#103—21no—
191C3×#103—21no—
192C3×#103—21no—
193C3×#103—21no—
194C3×#103—21no—
195C3×#103—21no—
196C3×#103—21no—
197C3×#102—21no—
198C3×#101—22no—
199C3×#101—41no—
200C3×C22⋊C8—21no—
201C3×C22⋊C8—21no—
202C3×#95—22no—
203C3×#95—22no—
204C2×#137C22×C311yescharacteristic
205C22×M16C22×C311yescharacteristic
206#556—21no—
207#554—21no—
208#552—21no—
209#552—22no—
210#552—21no—
211#551—22no—
212#544C22×C311yescharacteristic
213#542—21no—
214#541—21no—
215#536C22×C311yescharacteristic
216#533—21no—
217C2×C4⋊Q8C22×C311yescharacteristic
218#529—21no—
219#525C22×C311yescharacteristic
220C2×C22⋊Q8C22×C311yescharacteristic
221C2×C22⋊Q8C22×C311yescharacteristic
222#520C22×C311yescharacteristic
223#519C22×C311yescharacteristic
224C2×#117C22×C311yescharacteristic
225C22×C42C22×C311yescharacteristic
226#485—21no—
227#485—21no—
228#484—21no—
229#483—21no—
230#470—21no—
231#468—21no—
232#467—21no—
233#465—21no—
234#428C22×C311yescharacteristic
235#428C22×C311yescharacteristic
236#428C22×C311yescharacteristic
237C2×#104C22×C311yescharacteristic
238C2×#104C22×C311yescharacteristic
239#419C22×C311yescharacteristic
240#419C22×C311yescharacteristic
241#419C22×C311yescharacteristic
242#417C22×C311yescharacteristic
243C2×#101C22×C311yescharacteristic
244C2×#101C22×C311yescharacteristic
245#407C22×C311yescharacteristic
246#391C22×C311yescharacteristic
247#391C22×C311yescharacteristic
248#389—22no—
249#384C22×C311yescharacteristic
250#380—22no—
251#343C22×C311yescharacteristic
252#343C22×C311yescharacteristic
253#339C22×C311yescharacteristic
254#339C22×C311yescharacteristic
255#339C22×C311yescharacteristic
256#339C22×C311yescharacteristic
257#339C22×C311yescharacteristic
258#339C22×C311yescharacteristic
259C24×C3C2×D411yescharacteristic
260C3×#41—21no—
261C3×#41—21no—
262C3×#41—21no—
263C3×#41—21no—
264C2×C3×Q8—22no—
265C2×C3×Q8—21no—
266C2×C3×Q8—21no—
267C2×C3×Q8—21no—
268C2×C3×Q8—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—21no—
273C2×C3×Q8—21no—
274C2×C3×Q8—21no—
275C2×C3×Q8—21no—
276C2×C3×Q8—21no—
277C2×C3×Q8C2×D411yescharacteristic
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4C2×D411yescharacteristic
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—24no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—22no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—42no—
296C22×C3×C4—42no—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4C2×D412yes—
304C22×C3×C4C2411yescharacteristic
305C3×Q16—42no—
306C3×SD16—42no—
307C3×M16—21no—
308C3×M16—21no—
309C3×M16—21no—
310C3×M16—21no—
311C3×M16—21no—
312C3×M16—21no—
313C3×M16—21no—
314C3×M16—42no—
315C3×M16#4112yes—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—42no—
321C3×C4⋊C4—22no—
322C3×C4⋊C4—22no—
323C3×C4⋊C4—22no—
324C3×C4⋊C4—22no—
325C3×C4⋊C4—22no—
326C3×C4⋊C4—22no—
327C3×C4⋊C4—22no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—22no—
332C3×C4⋊C4—22no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—44no—
340C3×C4⋊C4—44no—
341C3×C4⋊C4—41no—
342C3×C4⋊C4—41no—
343C3×C4⋊C4C2×D411yescharacteristic
344C3×C4⋊C4C2×D411yescharacteristic
345C3×C4⋊C4C2×D411yescharacteristic
346C3×C4⋊C4C2×D411yescharacteristic
347C3×C4⋊C4C2×D411yescharacteristic
348C3×C4⋊C4C2×D411yescharacteristic
349C3×C22⋊C4—22no—
350C3×C22⋊C4—22no—
351C3×C22⋊C4—22no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—22no—
355C3×C22⋊C4—22no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—41no—
365C3×C42—22no—
366C3×C42—22no—
367C3×C42—22no—
368C3×C42—21no—
369C3×C42—21no—
370C3×C42—21no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—42no—
377C3×C42#4112yes—
378C2×#41C23×C311yescharacteristic
379C22×Q8C23×C311yescharacteristic
380C22×Q8C23×C311yescharacteristic
381C23×C4—21no—
382C23×C4C23×C311yescharacteristic
383#137—22no—
384#137—41no—
385C2×Q16—21no—
386C2×SD16—21no—
387C2×M16—21no—
388C2×M16—22no—
389C2×M16—41no—
390C2×M16C23×C311yescharacteristic
391C2×M16C23×C311yescharacteristic
392C2×M16C23×C311yescharacteristic
393C2×M16C23×C311yescharacteristic
394C22×C8—21no—
395C4⋊Q8—21no—
396C4⋊Q8—21no—
397C4⋊Q8—21no—
398C4⋊Q8—22no—
399C4⋊Q8—41no—
400#126—22no—
401#126—22no—
402#126—22no—
403#126—22no—
404#125—22no—
405#125—22no—
406#125—22no—
407#125—21no—
408#125—21no—
409#124—22no—
410#124—21no—
411#123—22no—
412#123—22no—
413#123—21no—
414#123—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—22no—
422C22⋊Q8—21no—
423C22⋊Q8—21no—
424C22⋊Q8—21no—
425C22⋊Q8—21no—
426C22⋊Q8—21no—
427C22⋊Q8—21no—
428C22⋊Q8C3×D411yescharacteristic
429C22⋊Q8C3×D411yescharacteristic
430#121C3×D411yescharacteristic
431#121C3×D411yescharacteristic
432#120—21no—
433C4×Q8—22no—
434C4×Q8—21no—
435C4×Q8—21no—
436C4×Q8—21no—
437C4×Q8—21no—
438C4×Q8—21no—
439C4×D4—22no—
440C4×D4—21no—
441C4×D4—22no—
442C4×D4—21no—
443C4×D4—21no—
444#117—22no—
445#117—22no—
446#117—21no—
447#117—21no—
448#117—22no—
449#117—21no—
450#117C3×D411yescharacteristic
451#117C3×D411yescharacteristic
452#117C23×C311yescharacteristic
453#117C23×C311yescharacteristic
454#117C23×C311yescharacteristic
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4C3×D412yes—
460C2×C4⋊C4C3×D411yescharacteristic
461C2×C4⋊C4C3×D411yescharacteristic
462C2×C4⋊C4C23×C311yescharacteristic
463C2×C4⋊C4C23×C311yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4C3×D412yes—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—41no—
471C2×C42C23×C311yescharacteristic
472C2×C42C23×C311yescharacteristic
473#107—21no—
474#107—21no—
475#107—21no—
476#106—21no—
477#106—21no—
478#106—21no—
479#104—22no—
480#104—41no—
481#103—21no—
482#103—21no—
483#103—21no—
484#103—21no—
485#103—21no—
486#103—21no—
487#103—21no—
488#102—21no—
489#101—22no—
490#101—41no—
491C22⋊C8—21no—
492C22⋊C8—21no—
493#95—22no—
494#95—22no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—22no—
498C23×C3—21no—
499C23×C3—41no—
500C23×C3#12011yescharacteristic
501C23×C3#12011yescharacteristic
502C23×C3C22×D411yescharacteristic
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—41no—
506C3×Q8—41no—
507C3×Q8—41no—
508C3×Q8—41no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×Q8—41no—
512C3×Q8—41no—
513C3×Q8—82no—
514C3×D4—21no—
515C3×D4—21no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—42no—
519C3×D4—81no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—22no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—22no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—48no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—42no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—42no—
552C2×C3×C4—42no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—81no—
558C2×C3×C4—82no—
559C2×C3×C4#12011yescharacteristic
560C2×C3×C4#12011yescharacteristic
561C2×C3×C4C22×D411yescharacteristic
562C2×C3×C4C22×D411yescharacteristic
563C2×C3×C4C2×#4111yescharacteristic
564C2×C3×C4C2×#4111yescharacteristic
565C2×C3×C4H(5,𝔽2)11yescharacteristic
566C2×C3×C42−1+411yescharacteristic
567C3×C8—22no—
568C3×C8—41no—
569C3×C8—41no—
570C3×C8—41no—
571C24C2×C3×D411yescharacteristic
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576C2×Q8—22no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8C2×C3×D411yescharacteristic
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4C2×C3×D411yescharacteristic
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4C2×C3×D412yes—
610C22×C4C2×C3×D411yescharacteristic
611C22×C4C2×C3×D411yescharacteristic
612C22×C4C2×C3×D411yescharacteristic
613C22×C4C2×C3×D411yescharacteristic
614C22×C4C2×C3×D411yescharacteristic
615C22×C4C2×C3×D412yes—
616C22×C4C24×C311yescharacteristic
617Q16—42no—
618SD16—42no—
619M16—21no—
620M16—21no—
621M16—21no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—42no—
627M16C3×#4112yes—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—42no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4C2×C3×D411yescharacteristic
656C4⋊C4C2×C3×D411yescharacteristic
657C4⋊C4C2×C3×D411yescharacteristic
658C4⋊C4C2×C3×D411yescharacteristic
659C4⋊C4C2×C3×D411yescharacteristic
660C4⋊C4C2×C3×D411yescharacteristic
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—42no—
689C42C3×#4112yes—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3#45612yes—
703C22×C3C2×#12011yescharacteristic
704C22×C3#54611yescharacteristic
705C22×C3#54711yescharacteristic
706C3×C4—24no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—42no—
710C3×C4—42no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—42no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—81no—
720C3×C4—81no—
721C3×C4#53211yescharacteristic
722C3×C4#53711yescharacteristic
723C3×C4#54611yescharacteristic
724C3×C4#54711yescharacteristic
725C23—22no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—41no—
730C23C3×#12011yescharacteristic
731C23C3×#12011yescharacteristic
732C23C22×C3×D411yescharacteristic
733Q8—21no—
734Q8—21no—
735Q8—41no—
736Q8—41no—
737Q8—41no—
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—82no—
744D4—21no—
745D4—21no—
746D4—42no—
747D4—41no—
748D4—41no—
749D4—81no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—48no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—81no—
788C2×C4—82no—
789C2×C4C3×#12011yescharacteristic
790C2×C4C3×#12011yescharacteristic
791C2×C4C22×C3×D411yescharacteristic
792C2×C4C22×C3×D411yescharacteristic
793C2×C4C2×C3×#4111yescharacteristic
794C2×C4C2×C3×#4111yescharacteristic
795C2×C4C3×H(5,𝔽2)11yescharacteristic
796C2×C4C3×2−1+411yescharacteristic
797C8—22no—
798C8—41no—
799C8—41no—
800C8—41no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—22no—
804C2×C3—41no—
805C2×C3—81no—
806C2×C3#243011yescharacteristic
807C2×C3C2×#45611yescharacteristic
808C2×C3#301811yescharacteristic
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22C3×#45612yes—
822C22C2×C3×#12011yescharacteristic
823C22C3×#54611yescharacteristic
824C22C3×#54711yescharacteristic
825C4—24no—
826C4—21no—
827C4—21no—
828C4—42no—
829C4—42no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—81no—
839C4—81no—
840C4C3×#53211yescharacteristic
841C4C3×#53711yescharacteristic
842C4C3×#54611yescharacteristic
843C4C3×#54711yescharacteristic
844C3#2552511yescharacteristic, direct product factor, Sylow
845C2—21no—
846C2—22no—
847C2—21no—
848C2—41no—
849C2—81no—
850C2C3×#243011yescharacteristic
851C2C2×C3×#45611yescharacteristic
852C2C3×#301811yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#525C22
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
2. C3×#3095C2semidirect
4. C3×#2857C2semidirect
5. C3×#2060C2semidirect
6. C3×#2038C2semidirect
7. C3×#2028C2semidirect
8. C3×#2005C2semidirect
9. C3×#1901C2semidirect
11. C3×#1886C2semidirect
12. C3×#1882C2semidirect
13. C3×#1859C2semidirect
14. C3×#1857C2semidirect
15. C2×C3×#339C2semidirect
16. #25525C3direct (N × H)
73. #3095C2×C3semidirect
75. #2857C2×C3semidirect
76. #2060C2×C3semidirect
77. #2038C2×C3semidirect
78. #2028C2×C3semidirect
79. #2005C2×C3semidirect
80. #1901C2×C3semidirect
82. #1886C2×C3semidirect
83. #1882C2×C3semidirect
84. #1859C2×C3semidirect
85. #1857C2×C3semidirect
86. C2×#339C2×C3semidirect
844. C3#25525direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#34952
C3×#30952
C3×#30562
C3×#28572
C3×#20602
C3×#20382
C3×#20282
C3×#20052
C3×#19012
C3×#18962
C3×#18862
C3×#18822
C3×#18592
C3×#18572
C2×C3×#3392
#255253