Finite Group Databasebeta

← C3×#25795 #10644402

Subgroups — C3×#25795 #10644402

Order 768.

1486 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#137C211yesmaximal, characteristic
2C2×C3×#497C211yesmaximal, characteristic, complemented
3C2×C3×#494C211yesmaximal, characteristic, complemented
4C2×C3×#470C211yesmaximal, characteristic, complemented
5C2×C3×#452C211yesmaximal, characteristic
6C2×C3×#451C211yesmaximal, characteristic, complemented
7C3×#2434C211yesmaximal, characteristic, complemented
8C3×#2432C211yesmaximal, characteristic
9C3×#2016C211yesmaximal, characteristic, complemented
10C3×#2016C211yesmaximal, characteristic, complemented
11C3×#2015C211yesmaximal, characteristic, complemented
12C3×#2013C211yesmaximal, characteristic, complemented
13C3×#1971C211yesmaximal, characteristic, complemented
14C3×#1968C211yesmaximal, characteristic, complemented
15C3×#1753C211yesmaximal, characteristic, complemented
16#25795C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C2×C3×#137—24no—
20C2×C3×#137—24no—
21C2×C3×#137—24no—
22C22×C3×Q16C2211yescharacteristic
23C22×C3×Q16C2211yescharacteristic
24C22×C3×Q16C2211yescharacteristic
25C22×C3×Q16C2211yescharacteristic
26C22×C3×Q16C2211yescharacteristic
27C22×C3×Q16C2211yescharacteristic
28C22×C3×SD16C2211yescharacteristic
29C22×C3×SD16C2211yescharacteristic
30C22×C3×SD16C2211yescharacteristic
31C22×C3×M16C2211yescharacteristic
32C2×C3×C4⋊Q8C2211yescharacteristic
33C2×C3×C4⋊Q8C2211yescharacteristic
34C2×C3×C4⋊Q8C2211yescharacteristic
35C2×C3×#124C2211yescharacteristic
36C2×C3×C22⋊Q8C2211yescharacteristic
37C2×C3×C22⋊Q8C2211yescharacteristic
38C3×#497—24no—
39C3×#494—24no—
40C3×#470—24no—
41C3×#452—24no—
42C3×#451—24no—
43C2×C3×#106C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×#103C2211yescharacteristic
47C2×C3×#103C2211yescharacteristic
48C2×C3×#103C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C2×C3×C22⋊C8C2211yescharacteristic
51C2×C3×#97C2211yescharacteristic
52C2×C3×C4×C8C2211yescharacteristic
53C3×#395—22no—
54C3×#394—22no—
55C3×#391C2211yescharacteristic
56C3×#391C2211yescharacteristic
57C3×#391C2211yescharacteristic
58C3×#390C2211yescharacteristic
59C3×#385—22no—
60C3×#385—22no—
61C3×C4×C22⋊C4C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C22×#137C2×C311yescharacteristic
65C2×#497C2×C311yescharacteristic, complemented
66C2×#494C2×C311yescharacteristic, complemented
67C2×#470C2×C311yescharacteristic, complemented
68C2×#452C2×C311yescharacteristic
69C2×#451C2×C311yescharacteristic, complemented
70#2434C2×C311yescharacteristic, complemented
71#2432C2×C311yescharacteristic
72#2016C2×C311yescharacteristic, complemented
73#2016C2×C311yescharacteristic, complemented
74#2015C2×C311yescharacteristic, complemented
75#2013C2×C311yescharacteristic, complemented
76#1971C2×C311yescharacteristic, complemented
77#1968C2×C311yescharacteristic, complemented
78#1753C2×C311yescharacteristic, complemented
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C22×C3×Q8—21no—
86C22×C3×Q8—22no—
87C22×C3×Q8—22no—
88C22×C3×Q8—22no—
89C22×C3×Q8—22no—
90C22×C3×Q8—41no—
91C22×C3×Q8—41no—
92C22×C3×Q8C2311yescharacteristic
93C22×C3×Q8C2311yescharacteristic
94C22×C3×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×C3×Q8C2311yescharacteristic
97C22×C3×D4—21no—
98C22×C3×D4C2311yescharacteristic
99C23×C3×C4—21no—
100C23×C3×C4—21no—
101C23×C3×C4C2311yescharacteristic
102C3×#137—232no—
103C2×C3×Q16—22no—
104C2×C3×Q16—22no—
105C2×C3×Q16—22no—
106C2×C3×Q16—22no—
107C2×C3×Q16—22no—
108C2×C3×Q16—22no—
109C2×C3×Q16—22no—
110C2×C3×Q16—22no—
111C2×C3×Q16—22no—
112C2×C3×Q16—22no—
113C2×C3×Q16—22no—
114C2×C3×Q16—22no—
115C2×C3×Q16—22no—
116C2×C3×Q16—22no—
117C2×C3×Q16—41no—
118C2×C3×Q16—41no—
119C2×C3×Q16—41no—
120C2×C3×Q16D414yes—
121C2×C3×SD16—22no—
122C2×C3×SD16—22no—
123C2×C3×SD16—22no—
124C2×C3×SD16—22no—
125C2×C3×SD16—22no—
126C2×C3×SD16—22no—
127C2×C3×SD16—22no—
128C2×C3×SD16—41no—
129C2×C3×SD16D414yes—
130C2×C3×M16—22no—
131C2×C3×M16—22no—
132C2×C3×M16D414yes—
133C22×C3×C8C2311yescharacteristic
134C22×C3×C8C2311yescharacteristic
135C22×C3×C8C2311yescharacteristic
136C22×C3×C8C2311yescharacteristic
137C3×C4⋊Q8—22no—
138C3×C4⋊Q8—22no—
139C3×C4⋊Q8—22no—
140C3×C4⋊Q8—41no—
141C3×C4⋊Q8—41no—
142C3×C4⋊Q8—41no—
143C3×#124—22no—
144C3×#124—41no—
145C3×C22⋊Q8—22no—
146C3×C22⋊Q8—22no—
147C3×C22⋊Q8—22no—
148C3×C22⋊Q8—22no—
149C2×C3×C4⋊C4—21no—
150C2×C3×C4⋊C4—22no—
151C2×C3×C4⋊C4—22no—
152C2×C3×C4⋊C4—22no—
153C2×C3×C4⋊C4—21no—
154C2×C3×C4⋊C4C2311yescharacteristic
155C2×C3×C4⋊C4C2311yescharacteristic
156C2×C3×C22⋊C4—21no—
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4—22no—
159C2×C3×C22⋊C4—22no—
160C2×C3×C22⋊C4D412yes—
161C2×C3×C42C2311yescharacteristic
162C2×C3×C42C2311yescharacteristic
163C3×#106—22no—
164C3×#103—22no—
165C3×#103—22no—
166C3×#103—22no—
167C3×#103—22no—
168C3×#103—22no—
169C3×#102—22no—
170C3×C22⋊C8D414yes—
171C3×#97—22no—
172C3×C4×C8—22no—
173C3×#95—22no—
174C3×#95—22no—
175C3×#95—22no—
176C3×#95D412yes—
177C22×#41C22×C311yescharacteristic
178C23×Q8C22×C311yescharacteristic
179C2×#137—24no—
180C2×#137—24no—
181C2×#137—24no—
182C22×Q16C22×C311yescharacteristic
183C22×Q16C22×C311yescharacteristic
184C22×Q16C22×C311yescharacteristic
185C22×Q16C22×C311yescharacteristic
186C22×Q16C22×C311yescharacteristic
187C22×Q16C22×C311yescharacteristic
188C22×SD16C22×C311yescharacteristic
189C22×SD16C22×C311yescharacteristic
190C22×SD16C22×C311yescharacteristic
191C22×M16C22×C311yescharacteristic
192C2×C4⋊Q8C22×C311yescharacteristic
193C2×C4⋊Q8C22×C311yescharacteristic
194C2×C4⋊Q8C22×C311yescharacteristic
195C2×#124C22×C311yescharacteristic
196C2×C22⋊Q8C22×C311yescharacteristic
197C2×C22⋊Q8C22×C311yescharacteristic
198#497—24no—
199#494—24no—
200#470—24no—
201#452—24no—
202#451—24no—
203C2×#106C22×C311yescharacteristic
204C2×#103C22×C311yescharacteristic
205C2×#103C22×C311yescharacteristic
206C2×#103C22×C311yescharacteristic
207C2×#103C22×C311yescharacteristic
208C2×#103C22×C311yescharacteristic
209C2×#102C22×C311yescharacteristic
210C2×C22⋊C8C22×C311yescharacteristic
211C2×#97C22×C311yescharacteristic
212C2×C4×C8C22×C311yescharacteristic
213#395—22no—
214#394—22no—
215#391C22×C311yescharacteristic
216#391C22×C311yescharacteristic
217#391C22×C311yescharacteristic
218#390C22×C311yescharacteristic
219#385—22no—
220#385—22no—
221C4×C22⋊C4C22×C311yescharacteristic
222#336C22×C311yescharacteristic
223#336C22×C311yescharacteristic
224C24×C3—21no—
225C24×C3C2×D411yescharacteristic
226C3×#41—28no—
227C3×#41—44no—
228C3×#41—44no—
229C3×#41—44no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—28no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8—21no—
253C2×C3×Q8—21no—
254C2×C3×Q8—21no—
255C2×C3×Q8—21no—
256C2×C3×Q8—21no—
257C2×C3×Q8—21no—
258C2×C3×Q8—42no—
259C2×C3×Q8—42no—
260C2×C3×Q8—44no—
261C2×C3×Q8—44no—
262C2×C3×Q8—44no—
263C2×C3×Q8—42no—
264C2×C3×Q8C2×D412yes—
265C2×C3×Q8C2×D412yes—
266C2×C3×Q8C2×D412yes—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—42no—
273C2×C3×D4—42no—
274C2×C3×D4—42no—
275C2×C3×D4C2×D412yes—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—42no—
288C22×C3×C4—42no—
289C22×C3×C4—42no—
290C22×C3×C4—42no—
291C22×C3×C4—42no—
292C22×C3×C4—42no—
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2×D411yescharacteristic
295C22×C3×C4C2×D412yes—
296C22×C3×C4C2×D412yes—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2411yescharacteristic
299C3×Q16—28no—
300C3×Q16—28no—
301C3×Q16—44no—
302C3×Q16—44no—
303C3×Q16—44no—
304C3×Q16—44no—
305C3×SD16—28no—
306C3×SD16—28no—
307C3×SD16—44no—
308C3×M16—28no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8C2×D412yes—
316C2×C3×C8C2×D412yes—
317C2×C3×C8C2×D412yes—
318C2×C3×C8C2×D412yes—
319C2×C3×C8C2×D412yes—
320C2×C3×C8C2×D412yes—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—44no—
326C3×C4⋊C4—44no—
327C3×C4⋊C4—44no—
328C3×C4⋊C4—42no—
329C3×C4⋊C4—42no—
330C3×C22⋊C4—24no—
331C3×C22⋊C4—44no—
332C3×C22⋊C4—42no—
333C3×C22⋊C4—42no—
334C3×C22⋊C4—44no—
335C3×C42—21no—
336C3×C42—21no—
337C3×C42—21no—
338C3×C42—21no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—41no—
344C2×#41—41no—
345C22×Q8—21no—
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—41no—
351C22×Q8—41no—
352C22×Q8C23×C311yescharacteristic
353C22×Q8C23×C311yescharacteristic
354C22×Q8C23×C311yescharacteristic
355C22×Q8C23×C311yescharacteristic
356C22×Q8C23×C311yescharacteristic
357C22×D4—21no—
358C22×D4C23×C311yescharacteristic
359C23×C4—21no—
360C23×C4—21no—
361C23×C4C23×C311yescharacteristic
362#137—232no—
363C2×Q16—22no—
364C2×Q16—22no—
365C2×Q16—22no—
366C2×Q16—22no—
367C2×Q16—22no—
368C2×Q16—22no—
369C2×Q16—22no—
370C2×Q16—22no—
371C2×Q16—22no—
372C2×Q16—22no—
373C2×Q16—22no—
374C2×Q16—22no—
375C2×Q16—22no—
376C2×Q16—22no—
377C2×Q16—41no—
378C2×Q16—41no—
379C2×Q16—41no—
380C2×Q16C3×D414yes—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—22no—
388C2×SD16—41no—
389C2×SD16C3×D414yes—
390C2×M16—22no—
391C2×M16—22no—
392C2×M16C3×D414yes—
393C22×C8C23×C311yescharacteristic
394C22×C8C23×C311yescharacteristic
395C22×C8C23×C311yescharacteristic
396C22×C8C23×C311yescharacteristic
397C4⋊Q8—22no—
398C4⋊Q8—22no—
399C4⋊Q8—22no—
400C4⋊Q8—41no—
401C4⋊Q8—41no—
402C4⋊Q8—41no—
403#124—22no—
404#124—41no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4C23×C311yescharacteristic
415C2×C4⋊C4C23×C311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4C3×D412yes—
421C2×C42C23×C311yescharacteristic
422C2×C42C23×C311yescharacteristic
423#106—22no—
424#103—22no—
425#103—22no—
426#103—22no—
427#103—22no—
428#103—22no—
429#102—22no—
430C22⋊C8C3×D414yes—
431#97—22no—
432C4×C8—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95C3×D412yes—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—42no—
445C23×C3—42no—
446C23×C3#12712yes—
447C23×C3C22×D411yescharacteristic
448C3×Q8—22no—
449C3×Q8—22no—
450C3×Q8—22no—
451C3×Q8—22no—
452C3×Q8—22no—
453C3×Q8—22no—
454C3×Q8—48no—
455C3×Q8—41no—
456C3×Q8—41no—
457C3×Q8—41no—
458C3×Q8—41no—
459C3×Q8—41no—
460C3×Q8—41no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×Q8—41no—
464C3×Q8—41no—
465C3×Q8—41no—
466C3×Q8—41no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×D4—22no—
470C3×D4—22no—
471C3×D4—48no—
472C3×D4—41no—
473C3×D4—41no—
474C2×C3×C4—22no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—48no—
489C2×C3×C4—48no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—42no—
505C2×C3×C4—42no—
506C2×C3×C4#12712yes—
507C2×C3×C4#13714yescomplemented
508C2×C3×C4C22×D411yescharacteristic
509C2×C3×C4C22×D411yescharacteristic
510C2×C3×C4C22×D411yescharacteristic
511C2×C3×C4C22×D411yescharacteristic
512C2×C3×C4H(5,𝔽2)11yescharacteristic
513C2×C3×C4H(5,𝔽2)11yescharacteristic
514C3×C8—22no—
515C3×C8—22no—
516C3×C8—22no—
517C3×C8#12014yes—
518C24—21no—
519C24C2×C3×D411yescharacteristic
520#41—28no—
521#41—44no—
522#41—44no—
523#41—44no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—28no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8—44no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8—42no—
558C2×Q8C2×C3×D412yes—
559C2×Q8C2×C3×D412yes—
560C2×Q8C2×C3×D412yes—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4C2×C3×D412yes—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×C3×D412yes—
588C22×C4C2×C3×D411yescharacteristic
589C22×C4C2×C3×D412yes—
590C22×C4C2×C3×D412yes—
591C22×C4C2×C3×D412yes—
592C22×C4C24×C311yescharacteristic
593Q16—28no—
594Q16—28no—
595Q16—44no—
596Q16—44no—
597Q16—44no—
598Q16—44no—
599SD16—28no—
600SD16—28no—
601SD16—44no—
602M16—28no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8C2×C3×D412yes—
610C2×C8C2×C3×D412yes—
611C2×C8C2×C3×D412yes—
612C2×C8C2×C3×D412yes—
613C2×C8C2×C3×D412yes—
614C2×C8C2×C3×D412yes—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C22⋊C4—24no—
625C22⋊C4—44no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—44no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—44no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—82no—
643C22×C3C2×#12711yescharacteristic
644C22×C3D4211yescharacteristic
645C22×C3D4211yescharacteristic
646C22×C3C2×#13712yes—
647C22×C3#57812yes—
648C3×C4—22no—
649C3×C4—24no—
650C3×C4—42no—
651C3×C4—42no—
652C3×C4—42no—
653C3×C4—42no—
654C3×C4—81no—
655C3×C4—81no—
656C3×C4—81no—
657C3×C4—81no—
658C3×C4C2×#12011yescharacteristic
659C3×C4#53511yescharacteristic
660C3×C4D4211yescharacteristic
661C3×C4D4211yescharacteristic
662C23—22no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23C3×#12712yes—
672C23C22×C3×D411yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—22no—
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—48no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694D4—22no—
695D4—22no—
696D4—48no—
697D4—41no—
698D4—41no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—48no—
714C2×C4—48no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4C3×#12712yes—
732C2×C4C3×#13714yescomplemented
733C2×C4C22×C3×D411yescharacteristic
734C2×C4C22×C3×D411yescharacteristic
735C2×C4C22×C3×D411yescharacteristic
736C2×C4C22×C3×D411yescharacteristic
737C2×C4C3×H(5,𝔽2)11yescharacteristic
738C2×C4C3×H(5,𝔽2)11yescharacteristic
739C8—22no—
740C8—22no—
741C8—22no—
742C8C3×#12014yes—
743C2×C3—42no—
744C2×C3—82no—
745C2×C3#243311yescharacteristic
746C2×C3#315211yescharacteristic
747C2×C3#315611yescharacteristic
748C2×C3#327012yes—
749C2×C3#327612yes—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—44no—
757C22—81no—
758C22—81no—
759C22—82no—
760C22C2×C3×#12711yescharacteristic
761C22C3×D4211yescharacteristic
762C22C3×D4211yescharacteristic
763C22C2×C3×#13712yes—
764C22C3×#57812yes—
765C4—22no—
766C4—24no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4—81no—
775C4C2×C3×#12011yescharacteristic
776C4C3×#53511yescharacteristic
777C4C3×D4211yescharacteristic
778C4C3×D4211yescharacteristic
779C3#2579511yescharacteristic, direct product factor, Sylow
780C2—42no—
781C2—82no—
782C2C3×#243311yescharacteristic
783C2C3×#315211yescharacteristic
784C2C3×#315611yescharacteristic
785C2C3×#327012yes—
786C2C3×#327612yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#497C2semidirect
3. C2×C3×#494C2semidirect
4. C2×C3×#470C2semidirect
6. C2×C3×#451C2semidirect
7. C3×#2434C2semidirect
9. C3×#2016C2semidirect
10. C3×#2016C2semidirect
11. C3×#2015C2semidirect
12. C3×#2013C2semidirect
13. C3×#1971C2semidirect
14. C3×#1968C2semidirect
15. C3×#1753C2semidirect
16. #25795C3direct (N × H)
65. C2×#497C2×C3semidirect
66. C2×#494C2×C3semidirect
67. C2×#470C2×C3semidirect
69. C2×#451C2×C3semidirect
70. #2434C2×C3semidirect
72. #2016C2×C3semidirect
73. #2016C2×C3semidirect
74. #2015C2×C3semidirect
75. #2013C2×C3semidirect
76. #1971C2×C3semidirect
77. #1968C2×C3semidirect
78. #1753C2×C3semidirect
507. C2×C3×C4#137semidirect
732. C2×C4C3×#137semidirect
779. C3#25795direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1372
C2×C3×#4972
C2×C3×#4942
C2×C3×#4702
C2×C3×#4522
C2×C3×#4512
C3×#24342
C3×#24322
C3×#20162
C3×#20152
C3×#20132
C3×#19712
C3×#19682
C3×#17532
#257953