Finite Group Databasebeta

← C3×#25510 #10644117

Subgroups — C3×#25510 #10644117

Order 768.

1134 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#542C211yesmaximal, characteristic, complemented
2C2×C3×#468C211yesmaximal, characteristic, complemented
3C2×C3×#466C211yesmaximal, characteristic
4C3×#2624C211yesmaximal, characteristic, complemented
5C3×#2057C211yesmaximal, characteristic, complemented
6C3×#2042C211yesmaximal, characteristic, complemented
7C3×#2023C211yesmaximal, characteristic, complemented
8C3×#2012C211yesmaximal, characteristic, complemented
9C3×#1895C211yesmaximal, characteristic, complemented
10C3×#1892C211yesmaximal, characteristic, complemented
11C3×#1880C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic, complemented
13C3×#1863C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic, complemented
15C3×#1729C211yesmaximal, characteristic, complemented
16#25510C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C23×C3×C8C2211yescharacteristic
21C3×#542—24no—
22C3×#542—24no—
23C2×C3×C4⋊Q8C2211yescharacteristic
24C2×C3×#126—21no—
25C2×C3×#124—21no—
26C2×C3×#124C2211yescharacteristic
27C2×C3×#123—21no—
28C2×C3×C22⋊Q8—21no—
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×D4C2211yescharacteristic
34C2×C3×#117C2211yescharacteristic
35C3×#468—24no—
36C3×#466—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#107C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C3×#399—21no—
48C3×#397—21no—
49C3×#394—21no—
50C3×#394—21no—
51C3×#390C2211yescharacteristic
52C3×#390C2211yescharacteristic
53C3×#389C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#542C2×C311yescharacteristic, complemented
65C2×#468C2×C311yescharacteristic, complemented
66C2×#466C2×C311yescharacteristic
67#2624C2×C311yescharacteristic, complemented
68#2057C2×C311yescharacteristic, complemented
69#2042C2×C311yescharacteristic, complemented
70#2023C2×C311yescharacteristic, complemented
71#2012C2×C311yescharacteristic, complemented
72#1895C2×C311yescharacteristic, complemented
73#1892C2×C311yescharacteristic, complemented
74#1880C2×C311yescharacteristic, complemented
75#1879C2×C311yescharacteristic, complemented
76#1863C2×C311yescharacteristic, complemented
77#1862C2×C311yescharacteristic, complemented
78#1729C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C23×C3×C4C2311yescharacteristic
87C2×C3×SD16—22no—
88C2×C3×SD16—22no—
89C2×C3×SD16—41no—
90C2×C3×D8—22no—
91C2×C3×D8—22no—
92C2×C3×D8—41no—
93C2×C3×M16—22no—
94C2×C3×M16—22no—
95C2×C3×M16—41no—
96C22×C3×C8—22no—
97C22×C3×C8—22no—
98C22×C3×C8—41no—
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C3×C4⋊Q8—22no—
104C3×C4⋊Q8—22no—
105C3×#126—28no—
106C3×#124—28no—
107C3×#124—22no—
108C3×#124—22no—
109C3×#123—28no—
110C3×C22⋊Q8—28no—
111C3×C22⋊Q8—22no—
112C3×C22⋊Q8D414yes—
113C3×#121—22no—
114C3×#121—22no—
115C3×#121—22no—
116C3×#121D414yes—
117C3×C4×Q8—22no—
118C3×C4×Q8—22no—
119C3×C4×D4—22no—
120C3×C4×D4—22no—
121C3×#117—22no—
122C3×#117—22no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4D411yescharacteristic
129C2×C3×C4⋊C4D411yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4D411yescharacteristic
147C2×C3×C22⋊C4D411yescharacteristic
148C2×C3×C42—21no—
149C2×C3×C42C2311yescharacteristic
150C2×C3×C42C2311yescharacteristic
151C3×#107—22no—
152C3×#107—22no—
153C3×#103—22no—
154C3×#103—22no—
155C3×#103—41no—
156C3×#102—22no—
157C3×#102—22no—
158C3×#102—22no—
159C3×#102—22no—
160C3×#102—41no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C22×SD16C22×C311yescharacteristic
165C22×D8C22×C311yescharacteristic
166C22×M16C22×C311yescharacteristic
167C23×C8C22×C311yescharacteristic
168#542—24no—
169#542—24no—
170C2×C4⋊Q8C22×C311yescharacteristic
171C2×#126—21no—
172C2×#124—21no—
173C2×#124C22×C311yescharacteristic
174C2×#123—21no—
175C2×C22⋊Q8—21no—
176C2×C22⋊Q8C22×C311yescharacteristic
177C2×#121C22×C311yescharacteristic
178C2×#121C22×C311yescharacteristic
179C2×C4×Q8C22×C311yescharacteristic
180C2×C4×D4C22×C311yescharacteristic
181C2×#117C22×C311yescharacteristic
182#468—24no—
183#466—24no—
184C2×#107C22×C311yescharacteristic
185C2×#107C22×C311yescharacteristic
186C2×#103C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#102C22×C311yescharacteristic
190C2×#102C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194#399—21no—
195#397—21no—
196#394—21no—
197#394—21no—
198#390C22×C311yescharacteristic
199#390C22×C311yescharacteristic
200#389C22×C311yescharacteristic
201#389C22×C311yescharacteristic
202#380C22×C311yescharacteristic
203#340C22×C311yescharacteristic
204#340C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#336C22×C311yescharacteristic
208#336C22×C311yescharacteristic
209#336C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211C24×C3—21no—
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C2×C3×Q8—24no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—81no—
221C2×C3×Q8—81no—
222C2×C3×Q8C2×D412yes—
223C2×C3×D4—24no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—42no—
236C2×C3×D4—81no—
237C2×C3×D4—81no—
238C2×C3×D4—81no—
239C2×C3×D4—81no—
240C2×C3×D4C2×D412yes—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—24no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—81no—
253C22×C3×C4—81no—
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D412yes—
260C22×C3×C4C2×D412yes—
261C22×C3×C4C2411yescharacteristic
262C3×SD16—44no—
263C3×D8—44no—
264C3×M16—44no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—44no—
276C2×C3×C8#4112yes—
277C2×C3×C8#4112yes—
278C3×C4⋊C4—24no—
279C3×C4⋊C4—24no—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—22no—
282C3×C4⋊C4—22no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—81no—
292C3×C4⋊C4—81no—
293C3×C4⋊C4C2×D412yes—
294C3×C4⋊C4C2×D412yes—
295C3×C22⋊C4—24no—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—42no—
303C3×C22⋊C4—81no—
304C3×C22⋊C4—81no—
305C3×C22⋊C4—81no—
306C3×C22⋊C4—81no—
307C3×C22⋊C4—81no—
308C3×C42—24no—
309C3×C42—21no—
310C3×C42—21no—
311C3×C42—21no—
312C3×C42—21no—
313C22×Q8—21no—
314C22×Q8C23×C311yescharacteristic
315C22×D4—21no—
316C22×D4—21no—
317C22×D4C23×C311yescharacteristic
318C22×D4C23×C311yescharacteristic
319C23×C4—21no—
320C23×C4C23×C311yescharacteristic
321C2×SD16—22no—
322C2×SD16—22no—
323C2×SD16—41no—
324C2×D8—22no—
325C2×D8—22no—
326C2×D8—41no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16—41no—
330C22×C8—22no—
331C22×C8—22no—
332C22×C8—41no—
333C22×C8C23×C311yescharacteristic
334C22×C8C23×C311yescharacteristic
335C22×C8C23×C311yescharacteristic
336C22×C8C23×C311yescharacteristic
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339#126—28no—
340#124—28no—
341#124—22no—
342#124—22no—
343#123—28no—
344C22⋊Q8—28no—
345C22⋊Q8—22no—
346C22⋊Q8C3×D414yes—
347#121—22no—
348#121—22no—
349#121—22no—
350#121C3×D414yes—
351C4×Q8—22no—
352C4×Q8—22no—
353C4×D4—22no—
354C4×D4—22no—
355#117—22no—
356#117—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4C3×D411yescharacteristic
363C2×C4⋊C4C3×D411yescharacteristic
364C2×C4⋊C4C23×C311yescharacteristic
365C2×C4⋊C4C23×C311yescharacteristic
366C2×C4⋊C4C23×C311yescharacteristic
367C2×C4⋊C4C23×C311yescharacteristic
368C2×C4⋊C4C23×C311yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4C3×D411yescharacteristic
381C2×C22⋊C4C3×D411yescharacteristic
382C2×C42—21no—
383C2×C42C23×C311yescharacteristic
384C2×C42C23×C311yescharacteristic
385#107—22no—
386#107—22no—
387#103—22no—
388#103—22no—
389#103—41no—
390#102—22no—
391#102—22no—
392#102—22no—
393#102—22no—
394#102—41no—
395#95—21no—
396#95—21no—
397#95—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—22no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3#12012yes—
419C23×C3C22×D411yescharacteristic
420C3×Q8—22no—
421C3×Q8—22no—
422C3×Q8—41no—
423C3×Q8—41no—
424C3×Q8—84no—
425C3×D4—22no—
426C3×D4—22no—
427C3×D4—41no—
428C3×D4—41no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—41no—
433C3×D4—84no—
434C3×D4—84no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—84no—
472C2×C3×C4#12012yes—
473C2×C3×C4C22×D411yescharacteristic
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C2×#4111yescharacteristic
476C2×C3×C4C2×#4111yescharacteristic
477C2×C3×C4H(5,𝔽2)11yescharacteristic
478C2×C3×C42−1+411yescharacteristic
479C3×C8—22no—
480C3×C8—22no—
481C3×C8—41no—
482C3×C8—41no—
483C24—21no—
484C24—21no—
485C24C2×C3×D411yescharacteristic
486C2×Q8—24no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—81no—
493C2×Q8—81no—
494C2×Q8C2×C3×D412yes—
495C2×D4—24no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—42no—
508C2×D4—81no—
509C2×D4—81no—
510C2×D4—81no—
511C2×D4—81no—
512C2×D4C2×C3×D412yes—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4C2×C3×D411yescharacteristic
527C22×C4C2×C3×D411yescharacteristic
528C22×C4C2×C3×D411yescharacteristic
529C22×C4C2×C3×D411yescharacteristic
530C22×C4C2×C3×D411yescharacteristic
531C22×C4C2×C3×D412yes—
532C22×C4C2×C3×D412yes—
533C22×C4C24×C311yescharacteristic
534SD16—44no—
535D8—44no—
536M16—44no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—44no—
548C2×C8C3×#4112yes—
549C2×C8C3×#4112yes—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—81no—
564C4⋊C4—81no—
565C4⋊C4C2×C3×D412yes—
566C4⋊C4C2×C3×D412yes—
567C22⋊C4—24no—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—24no—
574C22⋊C4—42no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C22⋊C4—81no—
579C22⋊C4—81no—
580C42—24no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3C2×#12011yescharacteristic
607C22×C3#53211yescharacteristic
608C22×C3#53711yescharacteristic
609C22×C3#57611yescharacteristic
610C22×C3#57611yescharacteristic
611C22×C3#57711yescharacteristic
612C22×C3#57811yescharacteristic
613C3×C4—22no—
614C3×C4—42no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—81no—
622C3×C4—81no—
623C3×C4—81no—
624C3×C4#54611yescharacteristic
625C3×C4#54611yescharacteristic
626C3×C4#54711yescharacteristic
627C3×C4#54711yescharacteristic
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—22no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23C3×#12012yes—
649C23C22×C3×D411yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—41no—
653Q8—41no—
654Q8—84no—
655D4—22no—
656D4—22no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—84no—
664D4—84no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—84no—
702C2×C4C3×#12012yes—
703C2×C4C22×C3×D411yescharacteristic
704C2×C4C22×C3×D411yescharacteristic
705C2×C4C2×C3×#4111yescharacteristic
706C2×C4C2×C3×#4111yescharacteristic
707C2×C4C3×H(5,𝔽2)11yescharacteristic
708C2×C4C3×2−1+411yescharacteristic
709C8—22no—
710C8—22no—
711C8—41no—
712C8—41no—
713C2×C3—42no—
714C2×C3—82no—
715C2×C3—161no—
716C2×C3#243011yescharacteristic
717C2×C3#300811yescharacteristic
718C2×C3#301311yescharacteristic
719C2×C3#317511yescharacteristic
720C2×C3#317911yescharacteristic
721C2×C3#325711yescharacteristic
722C2×C3#326211yescharacteristic
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22C2×C3×#12011yescharacteristic
745C22C3×#53211yescharacteristic
746C22C3×#53711yescharacteristic
747C22C3×#57611yescharacteristic
748C22C3×#57611yescharacteristic
749C22C3×#57711yescharacteristic
750C22C3×#57811yescharacteristic
751C4—22no—
752C4—42no—
753C4—41no—
754C4—41no—
755C4—42no—
756C4—42no—
757C4—41no—
758C4—41no—
759C4—81no—
760C4—81no—
761C4—81no—
762C4C3×#54611yescharacteristic
763C4C3×#54611yescharacteristic
764C4C3×#54711yescharacteristic
765C4C3×#54711yescharacteristic
766C3#2551011yescharacteristic, direct product factor, Sylow
767C2—42no—
768C2—82no—
769C2—161no—
770C2C3×#243011yescharacteristic
771C2C3×#300811yescharacteristic
772C2C3×#301311yescharacteristic
773C2C3×#317511yescharacteristic
774C2C3×#317911yescharacteristic
775C2C3×#325711yescharacteristic
776C2C3×#326211yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#466C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#542C2semidirect
2. C2×C3×#468C2semidirect
4. C3×#2624C2semidirect
5. C3×#2057C2semidirect
6. C3×#2042C2semidirect
7. C3×#2023C2semidirect
8. C3×#2012C2semidirect
9. C3×#1895C2semidirect
10. C3×#1892C2semidirect
11. C3×#1880C2semidirect
12. C3×#1879C2semidirect
13. C3×#1863C2semidirect
14. C3×#1862C2semidirect
15. C3×#1729C2semidirect
16. #25510C3direct (N × H)
64. C2×#542C2×C3semidirect
65. C2×#468C2×C3semidirect
67. #2624C2×C3semidirect
68. #2057C2×C3semidirect
69. #2042C2×C3semidirect
70. #2023C2×C3semidirect
71. #2012C2×C3semidirect
72. #1895C2×C3semidirect
73. #1892C2×C3semidirect
74. #1880C2×C3semidirect
75. #1879C2×C3semidirect
76. #1863C2×C3semidirect
77. #1862C2×C3semidirect
78. #1729C2×C3semidirect
766. C3#25510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5422
C2×C3×#4682
C2×C3×#4662
C3×#26242
C3×#20572
C3×#20422
C3×#20232
C3×#20122
C3×#18952
C3×#18922
C3×#18802
C3×#18792
C3×#18632
C3×#18622
C3×#17292
#255103