Finite Group Databasebeta

← #15879450

Subgroups — #15879450

Order 3328.

1292 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic26C211yesmaximal, characteristic
2C2×#11718362C212yesmaximal, complemented
3#13115776C212yesmaximal, complemented
4#13115774C212yesmaximal, complemented
5#13115770C212yesmaximal, complemented
6#13114816C211yesmaximal, characteristic
7#13114814C211yesmaximal, characteristic
8#13114814C211yesmaximal, characteristic
9#13114600C211yesmaximal, characteristic
10C22⋊C8×Dic13C211yesmaximal, characteristic
11C13×#1749C211yesmaximal, characteristic
12C23×Dic26C411yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C22×C4⋊Dic13C411yescharacteristic
15C22×#6101C411yescharacteristic
16C22×#6101C411yescharacteristic
17C22×C4×Dic13C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19C2×C4×Dic26—28no—
20C2×C4×Dic26C411yescharacteristic
21C2×C4×Dic26C411yescharacteristic
22C2×C4×Dic26C411yescharacteristic
23C2×C4×Dic26C411yescharacteristic
24C2×C4×Dic26C2211yescharacteristic
25C2×C4×Dic26C2211yescharacteristic
26C2×C4×Dic26C2211yescharacteristic
27C2×C4×Dic26C2211yescharacteristic
28C2×C13×C22⋊C8C2211yescharacteristic
29C2×C13×C22⋊C8C2211yescharacteristic
30C2×C13×#97C2212yes—
31C2×C22⋊#1055C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×#88055C2212yes—
34C2×#88054C2212yes—
35C2×#88054C2212yes—
36C2×C8×Dic13C2212yes—
37C2×C4⋊#1055C2212yes—
38#11718362—28no—
39C13×#336C2212yes—
40#11718142C2212yes—
41#11718142C2212yes—
42#11718142C2212yes—
43#11718142C2212yes—
44#11718116C2212yes—
45C23×C4×C13C2×C411yescharacteristic
46C23×C4×C13C2×C411yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×Dic13C2×C411yescharacteristic
49C23×Dic13C2×C411yescharacteristic
50C23×Dic13C2×C411yescharacteristic
51C23×Dic13C2×C411yescharacteristic
52C22×Dic26—24no—
53C22×Dic26—24no—
54C22×Dic26—24no—
55C22×Dic26C2×C411yescharacteristic
56C22×Dic26C2×C411yescharacteristic
57C22×Dic26C2×C411yescharacteristic
58C22×Dic26C2×C411yescharacteristic
59C22×C8×C13C2312yes—
60C22×C8×C13C2312yes—
61C2×C42×C13—24no—
62C2×C42×C13C2×C411yescharacteristic
63C2×C42×C13C2×C411yescharacteristic
64C2×C42×C13C2311yescharacteristic
65C2×C42×C13C2311yescharacteristic
66C2×C4⋊Dic13—24no—
67C2×C4⋊Dic13C2×C411yescharacteristic
68C2×C4⋊Dic13C2×C411yescharacteristic
69C2×C4⋊Dic13C2×C411yescharacteristic
70C2×C4⋊Dic13C2×C411yescharacteristic
71C2×#6101—24no—
72C2×#6101—24no—
73C2×#6101C2×C411yescharacteristic
74C2×#6101C2×C411yescharacteristic
75C2×#6101C2×C411yescharacteristic
76C2×#6101C2×C411yescharacteristic
77C2×#6101C2×C411yescharacteristic
78C2×#6101C2×C411yescharacteristic
79C2×#6101C2×C411yescharacteristic
80C2×#6101C2×C411yescharacteristic
81C2×C4×Dic13—24no—
82C2×C4×Dic13—24no—
83C2×C4×Dic13C2×C411yescharacteristic
84C2×C4×Dic13C2×C411yescharacteristic
85C2×C4×Dic13C2×C411yescharacteristic
86C2×C4×Dic13C2×C411yescharacteristic
87C2×C4×Dic13C2311yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C2×C4×Dic13C2311yescharacteristic
91C22×#1055C2312yes—
92C22×#1055C2312yes—
93C4×Dic26—24no—
94C4×Dic26—24no—
95C4×Dic26—24no—
96C4×Dic26—24no—
97C4×Dic26—24no—
98C4×Dic26—24no—
99C4×Dic26—24no—
100C4×Dic26D418yes—
101C13×C22⋊C8—22no—
102C13×C22⋊C8Q814yescomplemented
103C13×#97—24no—
104C22⋊#1055—22no—
105C22⋊#1055—22no—
106#88055—24no—
107#88054—24no—
108#88054—24no—
109C8×Dic13—24no—
110C4⋊#1055—24no—
111#22510—131nomaximal, Sylow
112C24×C13C22×C411yescharacteristic
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—41no—
121C22×C4×C13C22×C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C411yescharacteristic
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C22×C411yescharacteristic
126C22×C4×C13C2×Q812yes—
127C22×C4×C13#4112yes—
128C22×C4×C13C2411yescharacteristic
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—41no—
139C22×Dic13—41no—
140C22×Dic13M1614yes—
141C22×Dic13C22×C411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C411yescharacteristic
149C2×Dic26—232no—
150C2×Dic26—22no—
151C2×Dic26—22no—
152C2×Dic26—22no—
153C2×Dic26—22no—
154C2×Dic26—22no—
155C2×Dic26—22no—
156C2×Dic26—22no—
157C2×Dic26—22no—
158C2×Dic26—22no—
159C2×Dic26—22no—
160C2×Dic26C22⋊C414yes—
161C2×Dic26M1614yes—
162C2×C8×C13—22no—
163C2×C8×C13—22no—
164C2×C8×C13—22no—
165C2×C8×C13—22no—
166C2×C8×C13—22no—
167C2×C8×C13C2×Q814yescomplemented
168C42×C13—22no—
169C42×C13—22no—
170C42×C13—22no—
171C42×C13C2×D414yes—
172C4⋊Dic13—22no—
173C4⋊Dic13—22no—
174C4⋊Dic13—22no—
175C4⋊Dic13C22⋊C414yes—
176#6101—22no—
177#6101—22no—
178#6101—22no—
179#6101—22no—
180#6101—22no—
181#6101—22no—
182#6101C22⋊C414yes—
183#6101C22⋊C414yes—
184C4×Dic13—22no—
185C4×Dic13—22no—
186C4×Dic13—22no—
187C4×Dic13—22no—
188C4×Dic13—22no—
189C4×Dic13—22no—
190C4×Dic13C2×D414yes—
191C4×Dic13C2×D414yes—
192C2×#1055—22no—
193C2×#1055—22no—
194C2×#1055—22no—
195C2×#1055—22no—
196C2×#1055—22no—
197C2×#1055—22no—
198C22×C4×Q8—131no—
199C2×#446—132no—
200#1985—132no—
201#1985—132no—
202#1984—132no—
203#1797—131no—
204#1797—131no—
205#1797—131no—
206#1749—131no—
207#1749D1311yescharacteristic
208C4×C22⋊C8—131no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13C4×Q812yes—
214C23×C13C2×M1612yes—
215C23×C13#13112yes—
216C23×C13C23×C411yescharacteristic
217C2×C4×C13—28no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—44no—
232C2×C4×C13C2×C22⋊C412yes—
233C2×C4×C13C2×C22⋊C412yes—
234C2×C4×C13C4×Q812yes—
235C2×C4×C13C2×M1612yes—
236C2×C4×C13C22×D412yes—
237C2×C4×C13C22×Q811yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C132−1+412yes—
240C2×Dic13—28no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—28no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—44no—
259C2×Dic13—44no—
260C2×Dic13C2×C22⋊C412yes—
261C2×Dic13C2×C22⋊C412yes—
262C2×Dic13C2×C22⋊C412yes—
263C2×Dic13C2×C22⋊C412yes—
264C2×Dic13C2×M1612yes—
265C2×Dic13C2×M1612yes—
266C2×Dic13C2×M1612yes—
267C2×Dic13C2×M1612yes—
268Dic26—28no—
269Dic26—28no—
270Dic26—28no—
271Dic26—28no—
272C8×C13—24no—
273C8×C13—42no—
274#1055—42no—
275#1055—42no—
276C23×Q8—131no—
277C2×C4×Q8—131no—
278C2×C4×Q8—131no—
279C2×C4×Q8—131no—
280C2×C4×Q8—131no—
281C2×C4×Q8—131no—
282C2×C4×Q8—131no—
283C2×C4×Q8—131no—
284C2×C4×Q8—131no—
285C2×C4×Q8—268no—
286C22×C4⋊C4—131no—
287C22×C4⋊C4—131no—
288C22×C4⋊C4—131no—
289C22×C42—131no—
290C22×C42—131no—
291C22×C42C2×D1311yescharacteristic
292#446—268no—
293C2×C4⋊C8—132no—
294C2×C4⋊C8—132no—
295C2×C4⋊C8—132no—
296C2×C22⋊C8—131no—
297C2×C22⋊C8—131no—
298C2×C22⋊C8C2×D1311yescharacteristic
299C2×C22⋊C8C2×D1311yescharacteristic
300C2×#97—132no—
301C2×#97C2×D1312yes—
302C2×C4×C8—132no—
303#336—132no—
304#336—132no—
305#336—132no—
306#336—132no—
307#336—132no—
308#336C2×D1312yes—
309C22×C13—22no—
310C22×C13—22no—
311C22×C13—22no—
312C22×C13—22no—
313C22×C13—22no—
314C22×C13—22no—
315C22×C13#44614yescomplemented
316C22×C13C22×C22⋊C411yescharacteristic
317C22×C13C2×C4×Q811yescharacteristic
318C22×C13#51911yescharacteristic
319C22×C13C22×M1611yescharacteristic
320C22×C13C22×M1611yescharacteristic
321C22×C13C2×#13111yescharacteristic
322C22×C13#56811yescharacteristic
323C4×C13—22no—
324C4×C13—22no—
325C4×C13—22no—
326C4×C13—22no—
327C4×C13—41no—
328C4×C13#54812yes—
329C4×C13D4×Q812yes—
330Dic13—22no—
331Dic13—22no—
332Dic13—22no—
333Dic13—22no—
334Dic13—22no—
335Dic13—41no—
336Dic13—41no—
337Dic13#40714yes—
338C22×Q8—131no—
339C22×Q8—131no—
340C22×Q8—131no—
341C22×Q8—131no—
342C22×Q8—264no—
343C22×Q8—264no—
344C22×Q8—264no—
345C23×C4—131no—
346C23×C4—131no—
347C23×C4—131no—
348C23×C4—131no—
349C23×C4C4×D1311yescharacteristic
350C23×C4C4×D1311yescharacteristic
351C23×C4C22×D1311yescharacteristic
352C22×C8—132no—
353C22×C8—132no—
354C22×C8C22×D1312yes—
355C22×C8C22×D1312yes—
356C4×Q8—138no—
357C4×Q8—264no—
358C4×Q8—264no—
359C4×Q8—264no—
360C4×Q8—264no—
361C4×Q8—264no—
362C4×Q8—264no—
363C4×Q8—264no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—264no—
377C2×C4⋊C4—264no—
378C2×C4⋊C4—264no—
379C2×C42—24no—
380C2×C42—131no—
381C2×C42—131no—
382C2×C42—131no—
383C2×C42—131no—
384C2×C42—131no—
385C2×C42—131no—
386C2×C42—131no—
387C2×C42—131no—
388C2×C42—264no—
389C2×C42—264no—
390C2×C42C4×D1311yescharacteristic
391C2×C42C4×D1311yescharacteristic
392C2×C42C22×D1311yescharacteristic
393C2×C42C22×D1311yescharacteristic
394C4⋊C8—264no—
395C4⋊C8—264no—
396C4⋊C8—264no—
397C22⋊C8—22no—
398C22⋊C8—262no—
399C22⋊C8—262no—
400C22⋊C8Dic2614yescomplemented
401#97—24no—
402#97—264no—
403C4×C8—264no—
404C2×C13—24no—
405C2×C13Q8×C22⋊C411yescharacteristic
406C2×C13C2×#40711yescharacteristic
407C2×C13#288011yescharacteristic
408C2×C13C2×#44611yescharacteristic
409C2×C13Q8×M1611yescharacteristic
410C2×C13#298311yescharacteristic
411C2×C13#298411yescharacteristic
412C24C2×C4×D1311yescharacteristic
413C2×Q8—134no—
414C2×Q8—134no—
415C2×Q8—262no—
416C2×Q8—262no—
417C2×Q8—262no—
418C2×Q8—262no—
419C2×Q8—262no—
420C2×Q8—262no—
421C2×Q8—262no—
422C2×Q8—262no—
423C2×Q8—2632no—
424C2×Q8—262no—
425C2×Q8—262no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4—131no—
435C22×C4—134no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—131no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—521no—
453C22×C4—521no—
454C22×C4C2×Dic2612yes—
455C22×C4C2×C4×D1311yescharacteristic
456C22×C4C2×C4×D1311yescharacteristic
457C22×C4C2×C4×D1311yescharacteristic
458C22×C4C2×C4×D1311yescharacteristic
459C22×C4C2×C4×D1311yescharacteristic
460C22×C4#612712yes—
461C22×C4C23×D1311yescharacteristic
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—262no—
468C2×C8—262no—
469C2×C8—262no—
470C2×C8—262no—
471C2×C8—262no—
472C2×C8—262no—
473C2×C8C2×Dic2614yescomplemented
474C4⋊C4—134no—
475C4⋊C4—134no—
476C4⋊C4—134no—
477C4⋊C4—262no—
478C4⋊C4—262no—
479C4⋊C4—262no—
480C4⋊C4—262no—
481C4⋊C4—262no—
482C4⋊C4—262no—
483C4⋊C4—262no—
484C4⋊C4—262no—
485C4⋊C4—262no—
486C42—22no—
487C42—22no—
488C42—22no—
489C42—134no—
490C42—134no—
491C42—262no—
492C42—262no—
493C42—262no—
494C42—262no—
495C42—262no—
496C42—262no—
497C42D4×D1314yes—
498C13#2251011yescharacteristic, complemented, Sylow
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23C4×Dic2612yes—
504C23M16×D1312yes—
505C23#8816112yes—
506C23C22×C4×D1311yescharacteristic
507Q8—268no—
508Q8—268no—
509Q8—268no—
510Q8—268no—
511C2×C4—28no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—44no—
526C2×C4—132no—
527C2×C4—132no—
528C2×C4—132no—
529C2×C4—132no—
530C2×C4—132no—
531C2×C4—132no—
532C2×C4—132no—
533C2×C4—132no—
534C2×C4—268no—
535C2×C4—268no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—524no—
553C2×C4—524no—
554C2×C4C4×Dic2612yes—
555C2×C4C22⋊C4×D1312yes—
556C2×C4C22⋊C4×D1312yes—
557C2×C4M16×D1312yes—
558C2×C4C22×Dic2611yescharacteristic
559C2×C4C2×#612711yescharacteristic
560C2×C4C2×D4×D1312yes—
561C2×C4#8825712yes—
562C8—24no—
563C8—42no—
564C8—522no—
565C8—522no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22#1171836214yescomplemented
573C22C2×C4×Dic2611yescharacteristic
574C22C2×C22⋊C4×D1311yescharacteristic
575C22#1171922111yescharacteristic
576C22C2×M16×D1311yescharacteristic
577C22C2×M16×D1311yescharacteristic
578C22C2×#8816111yescharacteristic
579C22#1171945011yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—134no—
586C4—262no—
587C4—262no—
588C4—262no—
589C4—262no—
590C4—262no—
591C4—521no—
592C4—521no—
593C4D4×Dic2612yes—
594C4#1171925712yes—
595C2—24no—
596C2C22⋊C4×Dic2611yescharacteristic
597C2D13×#40711yescharacteristic
598C2#1312328611yescharacteristic
599C2C2×#1171836211yescharacteristic
600C2M16×Dic2611yescharacteristic
601C2#1312392011yescharacteristic
602C2#1312392611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1749C2
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenter#1749D13
hypocenterC13#22510
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C2×#11718362C2semidirect
3. #13115776C2semidirect
4. #13115774C2semidirect
5. #13115770C2semidirect
102. C13×C22⋊C8Q8semidirect
167. C2×C8×C13C2×Q8semidirect
315. C22×C13#446semidirect
400. C22⋊C8Dic26semidirect
473. C2×C8C2×Dic26semidirect
498. C13#22510semidirect
572. C22#11718362semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic262
C2×#117183622
#131157762
#131157742
#131157702
#131148162
#131148142
#131146002
C22⋊C8×Dic132
C13×#17492
#2251013