Finite Group Databasebeta

← C3×#25636 #10644243

Subgroups — C3×#25636 #10644243

Order 768.

1140 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#556C211yesmaximal, characteristic, complemented
2C2×C3×#495C211yesmaximal, characteristic
3C2×C3×#464C211yesmaximal, characteristic, complemented
4C3×#2592C211yesmaximal, characteristic, complemented
5C3×#2016C211yesmaximal, characteristic, complemented
6C3×#2015C211yesmaximal, characteristic, complemented
7C3×#2013C211yesmaximal, characteristic, complemented
8C3×#2012C211yesmaximal, characteristic
9C3×#1984C211yesmaximal, characteristic, complemented
10C3×#1983C211yesmaximal, characteristic, complemented
11C3×#1880C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic
13C3×#1878C211yesmaximal, characteristic, complemented
14C3×#1877C211yesmaximal, characteristic, complemented
15C3×C4×#103C211yesmaximal, characteristic, complemented
16#25636C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C22×C3×D8C2211yescharacteristic
23C3×#556—24no—
24C3×#556—24no—
25C2×C3×C4⋊Q8C2211yescharacteristic
26C2×C3×#126—21no—
27C2×C3×#126—21no—
28C2×C3×#124C2211yescharacteristic
29C2×C3×#124C2211yescharacteristic
30C2×C3×#124C2211yescharacteristic
31C2×C3×C22⋊Q8—21no—
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×Q8C2211yescharacteristic
34C2×C3×C4×Q8C2211yescharacteristic
35C2×C3×C4×D4C2211yescharacteristic
36C2×C3×#117—21no—
37C3×#495—24no—
38C3×#464—24no—
39C2×C3×C4⋊C8C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×C4×C8C2211yescharacteristic
49C3×#397—21no—
50C3×#393—21no—
51C3×#391C2211yescharacteristic
52C3×#391C2211yescharacteristic
53C3×#390C2211yescharacteristic
54C3×#390C2211yescharacteristic
55C3×#388—21no—
56C3×#388—21no—
57C3×C4×C4⋊C4C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#556C2×C311yescharacteristic, complemented
65C2×#495C2×C311yescharacteristic
66C2×#464C2×C311yescharacteristic, complemented
67#2592C2×C311yescharacteristic, complemented
68#2016C2×C311yescharacteristic, complemented
69#2015C2×C311yescharacteristic, complemented
70#2013C2×C311yescharacteristic, complemented
71#2012C2×C311yescharacteristic
72#1984C2×C311yescharacteristic, complemented
73#1983C2×C311yescharacteristic, complemented
74#1880C2×C311yescharacteristic, complemented
75#1879C2×C311yescharacteristic
76#1878C2×C311yescharacteristic, complemented
77#1877C2×C311yescharacteristic, complemented
78C4×#103C2×C311yescharacteristic, complemented
79C22×C3×Q8D411yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C2×C3×Q16—22no—
87C2×C3×Q16—22no—
88C2×C3×Q16—22no—
89C2×C3×Q16—41no—
90C2×C3×Q16—41no—
91C2×C3×Q16—41no—
92C2×C3×SD16—22no—
93C2×C3×SD16—22no—
94C2×C3×SD16—22no—
95C2×C3×SD16—22no—
96C2×C3×SD16—22no—
97C2×C3×SD16—41no—
98C2×C3×SD16—41no—
99C2×C3×SD16—41no—
100C2×C3×SD16—41no—
101C2×C3×D8—22no—
102C2×C3×D8—22no—
103C2×C3×D8—41no—
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C3×C4⋊Q8—22no—
109C3×C4⋊Q8—22no—
110C3×#126—28no—
111C3×#126—28no—
112C3×#124—22no—
113C3×#124—22no—
114C3×#124—22no—
115C3×#124—22no—
116C3×#124—22no—
117C3×#124D414yes—
118C3×C22⋊Q8—28no—
119C3×C4×Q8—22no—
120C3×C4×Q8—22no—
121C3×C4×Q8—22no—
122C3×C4×Q8—22no—
123C3×C4×Q8—22no—
124C3×C4×Q8D414yes—
125C3×C4×D4—22no—
126C3×C4×D4—22no—
127C3×#117—28no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4D411yescharacteristic
133C2×C3×C4⋊C4D411yescharacteristic
134C2×C3×C4⋊C4D411yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C42—21no—
150C2×C3×C42—21no—
151C2×C3×C42—21no—
152C2×C3×C42C2311yescharacteristic
153C2×C3×C42C2311yescharacteristic
154C2×C3×C42C2311yescharacteristic
155C3×C4⋊C8—22no—
156C3×#103—22no—
157C3×#103—22no—
158C3×#103—22no—
159C3×#103—41no—
160C3×#103—41no—
161C3×#102—22no—
162C3×#102—41no—
163C3×#102—41no—
164C3×C4×C8—22no—
165C3×#95—21no—
166C3×#95—21no—
167C3×#95—21no—
168C3×#95—21no—
169C3×#95—21no—
170C22×Q16C22×C311yescharacteristic
171C22×Q16C22×C311yescharacteristic
172C22×SD16C22×C311yescharacteristic
173C22×SD16C22×C311yescharacteristic
174C22×SD16C22×C311yescharacteristic
175C22×D8C22×C311yescharacteristic
176#556—24no—
177#556—24no—
178C2×C4⋊Q8C22×C311yescharacteristic
179C2×#126—21no—
180C2×#126—21no—
181C2×#124C22×C311yescharacteristic
182C2×#124C22×C311yescharacteristic
183C2×#124C22×C311yescharacteristic
184C2×C22⋊Q8—21no—
185C2×C4×Q8C22×C311yescharacteristic
186C2×C4×Q8C22×C311yescharacteristic
187C2×C4×Q8C22×C311yescharacteristic
188C2×C4×D4C22×C311yescharacteristic
189C2×#117—21no—
190#495—24no—
191#464—24no—
192C2×C4⋊C8C22×C311yescharacteristic
193C2×#103C22×C311yescharacteristic
194C2×#103C22×C311yescharacteristic
195C2×#103C22×C311yescharacteristic
196C2×#103C22×C311yescharacteristic
197C2×#103C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×#102C22×C311yescharacteristic
200C2×#102C22×C311yescharacteristic
201C2×C4×C8C22×C311yescharacteristic
202#397—21no—
203#393—21no—
204#391C22×C311yescharacteristic
205#391C22×C311yescharacteristic
206#390C22×C311yescharacteristic
207#390C22×C311yescharacteristic
208#388—21no—
209#388—21no—
210C4×C4⋊C4C22×C311yescharacteristic
211#340C22×C311yescharacteristic
212#340C22×C311yescharacteristic
213#336C22×C311yescharacteristic
214#336C22×C311yescharacteristic
215#336C22×C311yescharacteristic
216#336C22×C311yescharacteristic
217C24×C3—21no—
218C24×C3—21no—
219C2×C3×Q8—22no—
220C2×C3×Q8—22no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—41no—
238C2×C3×Q8C2×D412yes—
239C2×C3×Q8C2×D412yes—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4C2×D412yes—
252C22×C3×C4—24no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—42no—
260C22×C3×C4—42no—
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C3×Q16—44no—
269C3×Q16—44no—
270C3×SD16—44no—
271C3×SD16—44no—
272C3×SD16—44no—
273C3×D8—44no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8#4112yes—
285C2×C3×C8#4112yes—
286C3×C4⋊C4—24no—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—24no—
289C3×C4⋊C4—24no—
290C3×C4⋊C4—22no—
291C3×C4⋊C4—22no—
292C3×C4⋊C4—22no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4C2×D412yes—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—24no—
304C3×C22⋊C4—42no—
305C3×C22⋊C4—42no—
306C3×C22⋊C4—42no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4—81no—
309C3×C22⋊C4—81no—
310C3×C42—24no—
311C3×C42—24no—
312C3×C42—21no—
313C3×C42—21no—
314C3×C42—21no—
315C3×C42—21no—
316C3×C42—81no—
317C3×C42C2×D412yes—
318C3×C42C2×D412yes—
319C22×Q8C3×D411yescharacteristic
320C22×Q8C23×C311yescharacteristic
321C22×Q8C23×C311yescharacteristic
322C22×Q8C23×C311yescharacteristic
323C22×D4C23×C311yescharacteristic
324C22×D4C23×C311yescharacteristic
325C23×C4—21no—
326C2×Q16—22no—
327C2×Q16—22no—
328C2×Q16—22no—
329C2×Q16—41no—
330C2×Q16—41no—
331C2×Q16—41no—
332C2×SD16—22no—
333C2×SD16—22no—
334C2×SD16—22no—
335C2×SD16—22no—
336C2×SD16—22no—
337C2×SD16—41no—
338C2×SD16—41no—
339C2×SD16—41no—
340C2×SD16—41no—
341C2×D8—22no—
342C2×D8—22no—
343C2×D8—41no—
344C22×C8C23×C311yescharacteristic
345C22×C8C23×C311yescharacteristic
346C22×C8C23×C311yescharacteristic
347C22×C8C23×C311yescharacteristic
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350#126—28no—
351#126—28no—
352#124—22no—
353#124—22no—
354#124—22no—
355#124—22no—
356#124—22no—
357#124C3×D414yes—
358C22⋊Q8—28no—
359C4×Q8—22no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8C3×D414yes—
365C4×D4—22no—
366C4×D4—22no—
367#117—28no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4C3×D411yescharacteristic
373C2×C4⋊C4C3×D411yescharacteristic
374C2×C4⋊C4C3×D411yescharacteristic
375C2×C4⋊C4C23×C311yescharacteristic
376C2×C4⋊C4C23×C311yescharacteristic
377C2×C4⋊C4C23×C311yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42C23×C311yescharacteristic
393C2×C42C23×C311yescharacteristic
394C2×C42C23×C311yescharacteristic
395C4⋊C8—22no—
396#103—22no—
397#103—22no—
398#103—22no—
399#103—41no—
400#103—41no—
401#102—22no—
402#102—41no—
403#102—41no—
404C4×C8—22no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410C23×C3—22no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3C22×D411yescharacteristic
425C3×Q8—22no—
426C3×Q8—22no—
427C3×Q8—22no—
428C3×Q8—22no—
429C3×Q8—44no—
430C3×Q8—41no—
431C3×Q8—41no—
432C3×Q8—41no—
433C3×Q8—41no—
434C3×Q8—41no—
435C3×Q8—41no—
436C3×Q8—41no—
437C3×Q8—41no—
438C3×D4—22no—
439C3×D4—22no—
440C3×D4—41no—
441C3×D4—41no—
442C3×D4—41no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4—41no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—48no—
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—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4#12012yes—
481C2×C3×C4#12012yes—
482C2×C3×C4#13512yes—
483C2×C3×C4C22×D411yescharacteristic
484C2×C3×C4C22×D411yescharacteristic
485C2×C3×C4C2×#4111yescharacteristic
486C2×C3×C4C2×#4111yescharacteristic
487C2×C3×C4H(5,𝔽2)11yescharacteristic
488C2×C3×C4H(5,𝔽2)11yescharacteristic
489C3×C8—22no—
490C3×C8—22no—
491C3×C8—41no—
492C3×C8—41no—
493C24—21no—
494C24—21no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—41no—
514C2×Q8C2×C3×D412yes—
515C2×Q8C2×C3×D412yes—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4C2×C3×D412yes—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4C2×C3×D411yescharacteristic
538C22×C4C2×C3×D411yescharacteristic
539C22×C4C2×C3×D411yescharacteristic
540C22×C4C2×C3×D411yescharacteristic
541C22×C4C2×C3×D411yescharacteristic
542C22×C4C2×C3×D411yescharacteristic
543C22×C4C24×C311yescharacteristic
544Q16—44no—
545Q16—44no—
546SD16—44no—
547SD16—44no—
548SD16—44no—
549D8—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8C3×#4112yes—
561C2×C8C3×#4112yes—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4C2×C3×D412yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C42—24no—
587C42—24no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—81no—
593C42C2×C3×D412yes—
594C42C2×C3×D412yes—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
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×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3C2×#12011yescharacteristic
610C22×C3#55011yescharacteristic
611C22×C3#55011yescharacteristic
612C22×C3C2×#13511yescharacteristic
613C22×C3#57511yescharacteristic
614C22×C3#57711yescharacteristic
615C22×C3#57811yescharacteristic
616C3×C4—22no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4—42no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—81no—
626C3×C4—81no—
627C3×C4—81no—
628C3×C4#53211yescharacteristic
629C3×C4#53511yescharacteristic
630C3×C4#54611yescharacteristic
631C3×C4#54611yescharacteristic
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23C22×C3×D411yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—22no—
650Q8—22no—
651Q8—44no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660D4—22no—
661D4—22no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
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—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—48no—
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—41no—
702C2×C4C3×#12012yes—
703C2×C4C3×#12012yes—
704C2×C4C3×#13512yes—
705C2×C4C22×C3×D411yescharacteristic
706C2×C4C22×C3×D411yescharacteristic
707C2×C4C2×C3×#4111yescharacteristic
708C2×C4C2×C3×#4111yescharacteristic
709C2×C4C3×H(5,𝔽2)11yescharacteristic
710C2×C4C3×H(5,𝔽2)11yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C2×C3—82no—
716C2×C3—161no—
717C2×C3#243111yescharacteristic
718C2×C3#300211yescharacteristic
719C2×C3#301311yescharacteristic
720C2×C3#339311yescharacteristic
721C2×C3#339411yescharacteristic
722C2×C3#340111yescharacteristic
723C2×C3#340211yescharacteristic
724C22—42no—
725C22—42no—
726C22—42no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22C2×C3×#12011yescharacteristic
739C22C3×#55011yescharacteristic
740C22C3×#55011yescharacteristic
741C22C2×C3×#13511yescharacteristic
742C22C3×#57511yescharacteristic
743C22C3×#57711yescharacteristic
744C22C3×#57811yescharacteristic
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—41no—
751C4—42no—
752C4—41no—
753C4—41no—
754C4—81no—
755C4—81no—
756C4—81no—
757C4C3×#53211yescharacteristic
758C4C3×#53511yescharacteristic
759C4C3×#54611yescharacteristic
760C4C3×#54611yescharacteristic
761C3#2563611yescharacteristic, direct product factor, Sylow
762C2—82no—
763C2—161no—
764C2C3×#243111yescharacteristic
765C2C3×#300211yescharacteristic
766C2C3×#301311yescharacteristic
767C2C3×#339311yescharacteristic
768C2C3×#339411yescharacteristic
769C2C3×#340111yescharacteristic
770C2C3×#340211yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D8C22
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. C2×C3×#556C2semidirect
3. C2×C3×#464C2semidirect
4. C3×#2592C2semidirect
5. C3×#2016C2semidirect
6. C3×#2015C2semidirect
7. C3×#2013C2semidirect
9. C3×#1984C2semidirect
10. C3×#1983C2semidirect
11. C3×#1880C2semidirect
13. C3×#1878C2semidirect
14. C3×#1877C2semidirect
15. C3×C4×#103C2semidirect
16. #25636C3direct (N × H)
64. C2×#556C2×C3semidirect
66. C2×#464C2×C3semidirect
67. #2592C2×C3semidirect
68. #2016C2×C3semidirect
69. #2015C2×C3semidirect
70. #2013C2×C3semidirect
72. #1984C2×C3semidirect
73. #1983C2×C3semidirect
74. #1880C2×C3semidirect
76. #1878C2×C3semidirect
77. #1877C2×C3semidirect
78. C4×#103C2×C3semidirect
761. C3#25636direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5562
C2×C3×#4952
C2×C3×#4642
C3×#25922
C3×#20162
C3×#20152
C3×#20132
C3×#20122
C3×#19842
C3×#19832
C3×#18802
C3×#18792
C3×#18782
C3×#18772
C3×C4×#1032
#256363