Finite Group Databasebeta

← C3×#25775 #10644382

Subgroups — C3×#25775 #10644382

Order 768.

1580 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#135C211yesmaximal, characteristic, complemented
2C2×C3×#495C211yesmaximal, characteristic, complemented
3C2×C3×#492C211yesmaximal, characteristic, complemented
4C2×C3×#465C211yesmaximal, characteristic, complemented
5C2×C3×#452C211yesmaximal, characteristic, complemented
6C2×C3×#449C211yesmaximal, characteristic, complemented
7C3×#2432C211yesmaximal, characteristic, complemented
8C3×#2431C211yesmaximal, characteristic, complemented
9C3×#2016C211yesmaximal, characteristic, complemented
10C3×#2015C211yesmaximal, characteristic, complemented
11C3×#2012C211yesmaximal, characteristic, complemented
12C3×#2011C211yesmaximal, characteristic, complemented
13C3×#1968C211yesmaximal, characteristic, complemented
14C3×#1968C211yesmaximal, characteristic, complemented
15C3×C8×C22⋊C4C211yesmaximal, characteristic, complemented
16#25775C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×#41C2211yescharacteristic
19C2×C3×#135—24no—
20C2×C3×#135—24no—
21C2×C3×#135—24no—
22C22×C3×Q16C2211yescharacteristic
23C22×C3×Q16C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic
25C22×C3×SD16C2211yescharacteristic
26C22×C3×SD16C2211yescharacteristic
27C22×C3×SD16C2211yescharacteristic
28C22×C3×SD16C2211yescharacteristic
29C22×C3×D8C2211yescharacteristic
30C22×C3×D8C2211yescharacteristic
31C23×C3×C8C2211yescharacteristic
32C2×C3×C4⋊Q8C2211yescharacteristic
33C2×C3×#127C2211yescharacteristic
34C2×C3×#124C2211yescharacteristic
35C2×C3×#124C2211yescharacteristic
36C2×C3×C22⋊Q8C2211yescharacteristic
37C2×C3×#121C2211yescharacteristic
38C3×#495—24no—
39C3×#492—24no—
40C3×#465—24no—
41C3×#452—24no—
42C3×#449—24no—
43C2×C3×#106C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×#103C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C2×C3×C22⋊C8C2211yescharacteristic
51C2×C3×C4×C8C2211yescharacteristic
52C2×C3×C4×C8C2211yescharacteristic
53C3×#394—22no—
54C3×#392—22no—
55C3×#391C2211yescharacteristic
56C3×#391C2211yescharacteristic
57C3×#390C2211yescharacteristic
58C3×#390C2211yescharacteristic
59C3×#386—22no—
60C3×#385—22no—
61C3×C4×C22⋊C4C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C22×#135C2×C311yescharacteristic, complemented
65C2×#495C2×C311yescharacteristic, complemented
66C2×#492C2×C311yescharacteristic, complemented
67C2×#465C2×C311yescharacteristic, complemented
68C2×#452C2×C311yescharacteristic, complemented
69C2×#449C2×C311yescharacteristic, complemented
70#2432C2×C311yescharacteristic, complemented
71#2431C2×C311yescharacteristic, complemented
72#2016C2×C311yescharacteristic, complemented
73#2015C2×C311yescharacteristic, complemented
74#2012C2×C311yescharacteristic, complemented
75#2011C2×C311yescharacteristic, complemented
76#1968C2×C311yescharacteristic, complemented
77#1968C2×C311yescharacteristic, complemented
78C8×C22⋊C4C2×C311yescharacteristic, complemented
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—41no—
88C2×C3×#41—41no—
89C2×C3×#41—41no—
90C2×C3×#41—41no—
91C22×C3×Q8C2311yescharacteristic
92C22×C3×Q8C2311yescharacteristic
93C22×C3×Q8C2311yescharacteristic
94C22×C3×D4—21no—
95C22×C3×D4—21no—
96C22×C3×D4—21no—
97C22×C3×D4—22no—
98C22×C3×D4C2311yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C23×C3×C4—21no—
102C23×C3×C4—21no—
103C23×C3×C4C2311yescharacteristic
104C3×#135—232no—
105C2×C3×Q16—22no—
106C2×C3×Q16—22no—
107C2×C3×Q16—22no—
108C2×C3×Q16—22no—
109C2×C3×Q16—22no—
110C2×C3×Q16—41no—
111C2×C3×SD16—22no—
112C2×C3×SD16—22no—
113C2×C3×SD16—22no—
114C2×C3×SD16—22no—
115C2×C3×SD16—22no—
116C2×C3×SD16—22no—
117C2×C3×SD16—22no—
118C2×C3×SD16—22no—
119C2×C3×SD16—22no—
120C2×C3×SD16—22no—
121C2×C3×SD16—22no—
122C2×C3×SD16—41no—
123C2×C3×SD16—41no—
124C2×C3×SD16D414yescomplemented
125C2×C3×SD16D414yescomplemented
126C2×C3×D8—22no—
127C2×C3×D8—22no—
128C2×C3×D8—22no—
129C2×C3×D8—22no—
130C2×C3×D8—22no—
131C2×C3×D8—41no—
132C22×C3×C8—22no—
133C22×C3×C8—22no—
134C22×C3×C8D414yescomplemented
135C22×C3×C8C2311yescharacteristic
136C22×C3×C8C2311yescharacteristic
137C22×C3×C8C2311yescharacteristic
138C22×C3×C8C2311yescharacteristic
139C3×C4⋊Q8—22no—
140C3×C4⋊Q8—41no—
141C3×#127—22no—
142C3×#127—41no—
143C3×#124—22no—
144C3×#124—22no—
145C3×#124—41no—
146C3×#124—41no—
147C3×C22⋊Q8—22no—
148C3×C22⋊Q8—22no—
149C3×#121—22no—
150C3×#121—22no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4—22no—
153C2×C3×C4⋊C4C2311yescharacteristic
154C2×C3×C4⋊C4C2311yescharacteristic
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—22no—
157C2×C3×C22⋊C4—22no—
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—22no—
160C2×C3×C22⋊C4—22no—
161C2×C3×C22⋊C4D412yes—
162C2×C3×C42C2311yescharacteristic
163C2×C3×C42C2311yescharacteristic
164C3×#106—22no—
165C3×#103—22no—
166C3×#103—22no—
167C3×#103—22no—
168C3×#102—22no—
169C3×#102—22no—
170C3×#102—22no—
171C3×C22⋊C8D414yescomplemented
172C3×C4×C8—22no—
173C3×C4×C8—22no—
174C3×#95—22no—
175C3×#95—22no—
176C3×#95D412yes—
177C22×#41C22×C311yescharacteristic
178C22×#41C22×C311yescharacteristic
179C2×#135—24no—
180C2×#135—24no—
181C2×#135—24no—
182C22×Q16C22×C311yescharacteristic
183C22×Q16C22×C311yescharacteristic
184C22×SD16C22×C311yescharacteristic
185C22×SD16C22×C311yescharacteristic
186C22×SD16C22×C311yescharacteristic
187C22×SD16C22×C311yescharacteristic
188C22×SD16C22×C311yescharacteristic
189C22×D8C22×C311yescharacteristic
190C22×D8C22×C311yescharacteristic
191C23×C8C22×C311yescharacteristic
192C2×C4⋊Q8C22×C311yescharacteristic
193C2×#127C22×C311yescharacteristic
194C2×#124C22×C311yescharacteristic
195C2×#124C22×C311yescharacteristic
196C2×C22⋊Q8C22×C311yescharacteristic
197C2×#121C22×C311yescharacteristic
198#495—24no—
199#492—24no—
200#465—24no—
201#452—24no—
202#449—24no—
203C2×#106C22×C311yescharacteristic
204C2×#103C22×C311yescharacteristic
205C2×#103C22×C311yescharacteristic
206C2×#103C22×C311yescharacteristic
207C2×#102C22×C311yescharacteristic
208C2×#102C22×C311yescharacteristic
209C2×#102C22×C311yescharacteristic
210C2×C22⋊C8C22×C311yescharacteristic
211C2×C4×C8C22×C311yescharacteristic
212C2×C4×C8C22×C311yescharacteristic
213#394—22no—
214#392—22no—
215#391C22×C311yescharacteristic
216#391C22×C311yescharacteristic
217#390C22×C311yescharacteristic
218#390C22×C311yescharacteristic
219#386—22no—
220#385—22no—
221C4×C22⋊C4C22×C311yescharacteristic
222#336C22×C311yescharacteristic
223#336C22×C311yescharacteristic
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3C2×D411yescharacteristic
228C3×#41—28no—
229C3×#41—28no—
230C3×#41—44no—
231C3×#41—44no—
232C3×#41—44no—
233C3×#41—44no—
234C3×#41—44no—
235C3×#41—44no—
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×Q8C2×D412yes—
253C2×C3×Q8C2×D412yes—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—42no—
271C2×C3×D4—42no—
272C2×C3×D4—44no—
273C2×C3×D4—42no—
274C2×C3×D4—42no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
277C2×C3×D4—42no—
278C2×C3×D4—44no—
279C2×C3×D4—82no—
280C2×C3×D4—82no—
281C2×C3×D4C2×D412yes—
282C2×C3×D4C2×D412yes—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—42no—
293C22×C3×C4—42no—
294C22×C3×C4—42no—
295C22×C3×C4—42no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D412yes—
303C22×C3×C4C2411yescharacteristic
304C3×Q16—28no—
305C3×Q16—44no—
306C3×SD16—28no—
307C3×SD16—28no—
308C3×SD16—44no—
309C3×SD16—44no—
310C3×SD16—44no—
311C3×D8—28no—
312C3×D8—44no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—28no—
320C2×C3×C8C2×D412yes—
321C2×C3×C8C2×D412yes—
322C2×C3×C8C2×D412yes—
323C2×C3×C8C2×D412yes—
324C2×C3×C8C2×D412yes—
325C2×C3×C8C2×D412yes—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—44no—
331C3×C4⋊C4—42no—
332C3×C22⋊C4—24no—
333C3×C22⋊C4—44no—
334C3×C22⋊C4—44no—
335C3×C22⋊C4—42no—
336C3×C22⋊C4—42no—
337C3×C22⋊C4—44no—
338C3×C22⋊C4—82no—
339C3×C42—21no—
340C3×C42—21no—
341C3×C42—21no—
342C3×C42—21no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41—41no—
352C2×#41—41no—
353C2×#41—41no—
354C2×#41—41no—
355C22×Q8C23×C311yescharacteristic
356C22×Q8C23×C311yescharacteristic
357C22×Q8C23×C311yescharacteristic
358C22×D4—21no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—22no—
362C22×D4C23×C311yescharacteristic
363C22×D4C23×C311yescharacteristic
364C22×D4C23×C311yescharacteristic
365C23×C4—21no—
366C23×C4—21no—
367C23×C4C23×C311yescharacteristic
368#135—232no—
369C2×Q16—22no—
370C2×Q16—22no—
371C2×Q16—22no—
372C2×Q16—22no—
373C2×Q16—22no—
374C2×Q16—41no—
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16—22no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—41no—
387C2×SD16—41no—
388C2×SD16C3×D414yescomplemented
389C2×SD16C3×D414yescomplemented
390C2×D8—22no—
391C2×D8—22no—
392C2×D8—22no—
393C2×D8—22no—
394C2×D8—22no—
395C2×D8—41no—
396C22×C8—22no—
397C22×C8—22no—
398C22×C8C3×D414yescomplemented
399C22×C8C23×C311yescharacteristic
400C22×C8C23×C311yescharacteristic
401C22×C8C23×C311yescharacteristic
402C22×C8C23×C311yescharacteristic
403C4⋊Q8—22no—
404C4⋊Q8—41no—
405#127—22no—
406#127—41no—
407#124—22no—
408#124—22no—
409#124—41no—
410#124—41no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413#121—22no—
414#121—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4C23×C311yescharacteristic
418C2×C4⋊C4C23×C311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4C3×D412yes—
426C2×C42C23×C311yescharacteristic
427C2×C42C23×C311yescharacteristic
428#106—22no—
429#103—22no—
430#103—22no—
431#103—22no—
432#102—22no—
433#102—22no—
434#102—22no—
435C22⋊C8C3×D414yescomplemented
436C4×C8—22no—
437C4×C8—22no—
438#95—22no—
439#95—22no—
440#95C3×D412yes—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—42no—
452C23×C3—42no—
453C23×C3—42no—
454C23×C3—42no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—42no—
459C23×C3—42no—
460C23×C3#12712yes—
461C23×C3C22×D411yescharacteristic
462C3×Q8—22no—
463C3×Q8—22no—
464C3×Q8—22no—
465C3×Q8—22no—
466C3×Q8—41no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×Q8—41no—
470C3×Q8—41no—
471C3×Q8—41no—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×D4—22no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—22no—
478C3×D4—48no—
479C3×D4—48no—
480C3×D4—41no—
481C3×D4—41no—
482C3×D4—41no—
483C3×D4—41no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4—88no—
489C3×D4—84no—
490C2×C3×C4—22no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—48no—
504C2×C3×C4—48no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—42no—
515C2×C3×C4—42no—
516C2×C3×C4#12712yes—
517C2×C3×C4#13514yescomplemented
518C2×C3×C4C22×D411yescharacteristic
519C2×C3×C4C22×D411yescharacteristic
520C2×C3×C4C22×D411yescharacteristic
521C2×C3×C4C22×D411yescharacteristic
522C2×C3×C4H(5,𝔽2)11yescharacteristic
523C2×C3×C4H(5,𝔽2)11yescharacteristic
524C3×C8—22no—
525C3×C8—22no—
526C3×C8—22no—
527C3×C8#12014yes—
528C24—21no—
529C24—21no—
530C24—21no—
531C24C2×C3×D411yescharacteristic
532#41—28no—
533#41—28no—
534#41—44no—
535#41—44no—
536#41—44no—
537#41—44no—
538#41—44no—
539#41—44no—
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—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8C2×C3×D412yes—
557C2×Q8C2×C3×D412yes—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—44no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—44no—
583C2×D4—82no—
584C2×D4—82no—
585C2×D4C2×C3×D412yes—
586C2×D4C2×C3×D412yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4C2×C3×D412yes—
603C22×C4C2×C3×D411yescharacteristic
604C22×C4C2×C3×D412yes—
605C22×C4C2×C3×D412yes—
606C22×C4C2×C3×D412yes—
607C22×C4C24×C311yescharacteristic
608Q16—28no—
609Q16—44no—
610SD16—28no—
611SD16—28no—
612SD16—44no—
613SD16—44no—
614SD16—44no—
615D8—28no—
616D8—44no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—28no—
624C2×C8C2×C3×D412yes—
625C2×C8C2×C3×D412yes—
626C2×C8C2×C3×D412yes—
627C2×C8C2×C3×D412yes—
628C2×C8C2×C3×D412yes—
629C2×C8C2×C3×D412yes—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—44no—
635C4⋊C4—42no—
636C22⋊C4—24no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—44no—
642C22⋊C4—82no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—44no—
655C22×C3—44no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—82no—
661C22×C3—82no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—82no—
666C22×C3—82no—
667C22×C3C2×#12711yescharacteristic
668C22×C3D4211yescharacteristic
669C22×C3D4211yescharacteristic
670C22×C3C2×#13512yes—
671C22×C3#57712yes—
672C3×C4—22no—
673C3×C4—24no—
674C3×C4—42no—
675C3×C4—42no—
676C3×C4—42no—
677C3×C4—81no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4C2×#12011yescharacteristic
681C3×C4#53511yescharacteristic
682C3×C4D4211yescharacteristic
683C3×C4D4211yescharacteristic
684C23—22no—
685C23—22no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—42no—
699C23—42no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23C3×#12712yes—
704C23C22×C3×D411yescharacteristic
705Q8—22no—
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—41no—
710Q8—41no—
711Q8—41no—
712Q8—41no—
713Q8—41no—
714Q8—41no—
715Q8—41no—
716Q8—41no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—22no—
721D4—48no—
722D4—48no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—88no—
732D4—84no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—48no—
747C2×C4—48no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4C3×#12712yes—
760C2×C4C3×#13514yescomplemented
761C2×C4C22×C3×D411yescharacteristic
762C2×C4C22×C3×D411yescharacteristic
763C2×C4C22×C3×D411yescharacteristic
764C2×C4C22×C3×D411yescharacteristic
765C2×C4C3×H(5,𝔽2)11yescharacteristic
766C2×C4C3×H(5,𝔽2)11yescharacteristic
767C8—22no—
768C8—22no—
769C8—22no—
770C8C3×#12014yes—
771C2×C3—42no—
772C2×C3—82no—
773C2×C3—82no—
774C2×C3—161no—
775C2×C3#243311yescharacteristic
776C2×C3#314711yescharacteristic
777C2×C3#315411yescharacteristic
778C2×C3#328212yes—
779C2×C3#328412yes—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—44no—
788C22—44no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—82no—
794C22—82no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—82no—
799C22—82no—
800C22C2×C3×#12711yescharacteristic
801C22C3×D4211yescharacteristic
802C22C3×D4211yescharacteristic
803C22C2×C3×#13512yes—
804C22C3×#57712yes—
805C4—22no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—81no—
811C4—81no—
812C4—81no—
813C4C2×C3×#12011yescharacteristic
814C4C3×#53511yescharacteristic
815C4C3×D4211yescharacteristic
816C4C3×D4211yescharacteristic
817C3#2577511yescharacteristic, direct product factor, Sylow
818C2—42no—
819C2—82no—
820C2—82no—
821C2—161no—
822C2C3×#243311yescharacteristic
823C2C3×#314711yescharacteristic
824C2C3×#315411yescharacteristic
825C2C3×#328212yes—
826C2C3×#328412yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
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
1. C22×C3×#135C2semidirect
2. C2×C3×#495C2semidirect
3. C2×C3×#492C2semidirect
4. C2×C3×#465C2semidirect
5. C2×C3×#452C2semidirect
6. C2×C3×#449C2semidirect
7. C3×#2432C2semidirect
8. C3×#2431C2semidirect
9. C3×#2016C2semidirect
10. C3×#2015C2semidirect
11. C3×#2012C2semidirect
12. C3×#2011C2semidirect
13. C3×#1968C2semidirect
14. C3×#1968C2semidirect
15. C3×C8×C22⋊C4C2semidirect
16. #25775C3direct (N × H)
64. C22×#135C2×C3semidirect
65. C2×#495C2×C3semidirect
66. C2×#492C2×C3semidirect
67. C2×#465C2×C3semidirect
68. C2×#452C2×C3semidirect
69. C2×#449C2×C3semidirect
70. #2432C2×C3semidirect
71. #2431C2×C3semidirect
72. #2016C2×C3semidirect
73. #2015C2×C3semidirect
74. #2012C2×C3semidirect
75. #2011C2×C3semidirect
76. #1968C2×C3semidirect
77. #1968C2×C3semidirect
78. C8×C22⋊C4C2×C3semidirect
124. C2×C3×SD16D4semidirect
125. C2×C3×SD16D4semidirect
134. C22×C3×C8D4semidirect
171. C3×C22⋊C8D4semidirect
388. C2×SD16C3×D4semidirect
389. C2×SD16C3×D4semidirect
398. C22×C8C3×D4semidirect
435. C22⋊C8C3×D4semidirect
517. C2×C3×C4#135semidirect
760. C2×C4C3×#135semidirect
817. C3#25775direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1352
C2×C3×#4952
C2×C3×#4922
C2×C3×#4652
C2×C3×#4522
C2×C3×#4492
C3×#24322
C3×#24312
C3×#20162
C3×#20152
C3×#20122
C3×#20112
C3×#19682
C3×C8×C22⋊C42
#257753