Finite Group Databasebeta

← #15898479

Subgroups — #15898479

Order 3328.

1392 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718751C211yesmaximal, characteristic, complemented
2C2×#11718889C212yesmaximal, complemented
3C2×#11718691C211yesmaximal, characteristic, complemented
4#13119745C211yesmaximal, characteristic
5#13116029C212yesmaximal, complemented
6#13115844C212yesmaximal, complemented
7#13115657C211yesmaximal, characteristic, complemented
8#13115635C211yesmaximal, characteristic
9#13114851C211yesmaximal, characteristic, complemented
10#13114771C212yesmaximal, complemented
11C2×D4×Q8×C13C211yesmaximal, characteristic
12C23×Q8×C13C2212yes—
13D4×Q8×C13—24no—
14D4×Q8×C13—24no—
15C2×C13×C4⋊Q8—21no—
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8—22no—
18C2×C13×C22⋊Q8C2212yes—
19C2×C4×Q8×C13C2211yescharacteristic
20C2×C4×D4×C13—21no—
21C2×C4×D4×C13C2211yescharacteristic
22C22×#6107C2212yes—
23C22×#6107C2211yescharacteristic
24C2×#88178C2212yes—
25C2×C4×Dic26C2211yescharacteristic
26#11718889—28no—
27C2×#88075C2212yes—
28C2×#88075C2211yescharacteristic
29C2×#88075C2212yes—
30C2×#88075C2212yes—
31C2×#88075C2212yes—
32#11718883—21no—
33#11718873C2212yes—
34C2×C22⋊#1055C2212yes—
35C2×C22⋊#1055C2212yes—
36#11718751—24no—
37#11718691—24no—
38#11718641—21no—
39C2×#88050C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41#11718605—22no—
42#11718597C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45#11718121C2212yes—
46C22×Q8×C13—24no—
47C22×Q8×C13—24no—
48C22×Q8×C13—22no—
49C22×Q8×C13—24no—
50C22×Q8×C13—24no—
51C22×Q8×C13—42no—
52C22×Q8×C13—42no—
53C22×Q8×C13C2312yes—
54C22×Q8×C13C2311yescharacteristic
55C22×D4×C13D411yescharacteristic
56C23×C4×C13—22no—
57C23×C4×C13C2312yes—
58C22×Dic26C2311yescharacteristic
59C13×C4⋊Q8—28no—
60C13×C4⋊Q8—22no—
61C13×C4⋊Q8D414yes—
62C13×C22⋊Q8—216no—
63C13×C22⋊Q8—24no—
64C13×C22⋊Q8—24no—
65C4×Q8×C13—22no—
66C4×Q8×C13D414yes—
67C4×D4×C13—28no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4D411yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4D412yes—
78C2×C42×C13—21no—
79C2×C42×C13C2311yescharacteristic
80C2×C22⋊Dic13—22no—
81C2×C22⋊Dic13—22no—
82C2×#6107—22no—
83C2×#6107—22no—
84C2×#6107—24no—
85C2×#6107—24no—
86C2×#6107—42no—
87C2×#6107D414yescomplemented
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2312yes—
90#88178—24no—
91#88178—42no—
92C2×#6101—21no—
93C2×#6101—22no—
94C2×C4×Dic13—21no—
95C22×#1055C2312yes—
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C4×Dic26—22no—
99C4×Dic26—22no—
100#88075—22no—
101#88075—24no—
102#88075—24no—
103#88075—24no—
104#88075—42no—
105#88071—21no—
106#88071—21no—
107#88071—22no—
108C22⋊#1055—24no—
109C22⋊#1055—42no—
110#88050—22no—
111#88048—22no—
112C4⋊#1055—22no—
113#88043—22no—
114#24255—131nomaximal, Sylow
115C24×C13C2×D412yes—
116C2×Q8×C13—28no—
117C2×Q8×C13—21no—
118C2×Q8×C13—22no—
119C2×Q8×C13—21no—
120C2×Q8×C13—21no—
121C2×Q8×C13—22no—
122C2×Q8×C13—22no—
123C2×Q8×C13—22no—
124C2×Q8×C13—22no—
125C2×Q8×C13—44no—
126C2×Q8×C13—44no—
127C2×Q8×C13—48no—
128C2×Q8×C13—48no—
129C2×Q8×C13—48no—
130C2×Q8×C13—48no—
131C2×Q8×C13C2×D412yes—
132C2×Q8×C13C2×D414yes—
133C2×Q8×C13C2×D412yes—
134C2×Q8×C13#4112yes—
135C2×D4×C13—24no—
136C2×D4×C13—22no—
137C22×C4×C13—21no—
138C22×C4×C13—28no—
139C22×C4×C13—21no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—44no—
148C22×C4×C13—44no—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2411yescharacteristic
153C22×Dic13—21no—
154C22×Dic13—22no—
155C22×Dic13—21no—
156C2×Dic26—21no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26C2×D412yes—
162C13×C4⋊C4—28no—
163C13×C4⋊C4—24no—
164C13×C4⋊C4—24no—
165C13×C4⋊C4—24no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4C2×D412yes—
169C13×C22⋊C4—28no—
170C13×C22⋊C4—24no—
171C42×C13—24no—
172C42×C13C2×D412yes—
173C42×C13C2×D412yes—
174C22⋊Dic13—44no—
175C22⋊Dic13—44no—
176#6107—28no—
177#6107—48no—
178C4⋊Dic13—21no—
179C4⋊Dic13—22no—
180C4⋊Dic13—21no—
181C4⋊Dic13—22no—
182#6101—44no—
183#6101—42no—
184C4×Dic13—42no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—22no—
192C2×#1055—21no—
193C2×#1055C2×D412yes—
194C2×D4×Q8D1311yescharacteristic
195C2×#462—131no—
196C2×#451—132no—
197C2×#441—131no—
198#2536—131no—
199#2035—132no—
200#2001—132no—
201#1960—131no—
202#1955—131no—
203#1805—131no—
204#1787—132no—
205C23×C13—22no—
206C23×C13—22no—
207C23×C13—22no—
208C23×C13—22no—
209C23×C13—22no—
210C23×C13—22no—
211C23×C13#13714yes—
212C23×C13C22×D411yescharacteristic
213Q8×C13—22no—
214Q8×C13—22no—
215Q8×C13—22no—
216Q8×C13—24no—
217Q8×C13—24no—
218Q8×C13—416no—
219Q8×C13—42no—
220Q8×C13—42no—
221Q8×C13#12114yes—
222D4×C13—28no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—24no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—416no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13#12012yes—
242C2×C4×C13#12012yes—
243C2×C4×C13C22×D411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13H(5,𝔽2)11yescharacteristic
248C2×C4×C13H(5,𝔽2)11yescharacteristic
249C2×Dic13—22no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257Dic26—22no—
258Dic26—22no—
259Dic26—41no—
260Dic26—41no—
261#1055—22no—
262#1055—41no—
263#1055—42no—
264C23×Q8C2×D1312yes—
265C22×Q16—131no—
266C22×Q16—132no—
267D4×Q8—24no—
268D4×Q8—24no—
269C2×C4⋊Q8—21no—
270C2×C4⋊Q8C2×D1311yescharacteristic
271C2×C22⋊Q8—22no—
272C2×C22⋊Q8—132no—
273C2×C22⋊Q8C2×D1312yes—
274C2×C4×Q8—131no—
275C2×C4×Q8C2×D1311yescharacteristic
276C2×C4×D4—21no—
277C2×C4×D4C2×D1311yescharacteristic
278#462—264no—
279#451—268no—
280#441—264no—
281C2×#106—131no—
282C2×C4⋊C8—131no—
283C2×#103—132no—
284C2×#103—131no—
285C2×#103—132no—
286C2×#103—132no—
287C2×#103—131no—
288C2×#103—132no—
289C2×C22⋊C8—132no—
290C2×C22⋊C8—132no—
291C2×#97—131no—
292#398—261no—
293#394—261no—
294#388—262no—
295#382—131no—
296#380—132no—
297#340—132no—
298C22×C13—24no—
299C22×C13—24no—
300C22×C13—24no—
301C22×C13—42no—
302C22×C13—42no—
303C22×C13—42no—
304C22×C13—42no—
305C22×C13C2×#12011yescharacteristic
306C22×C13D4211yescharacteristic
307C22×C13#54611yescharacteristic
308C22×C13C2×#13712yes—
309C22×C13#57812yes—
310C4×C13—24no—
311C4×C13—22no—
312C4×C13—22no—
313C4×C13—42no—
314C4×C13—44no—
315C4×C13—42no—
316C4×C13C2×#12111yescharacteristic
317C4×C13#53511yescharacteristic
318C4×C13D4211yescharacteristic
319C4×C13#54611yescharacteristic
320Dic13—42no—
321Dic13—81no—
322Dic13—82no—
323C22×Q8—24no—
324C22×Q8—24no—
325C22×Q8—22no—
326C22×Q8—24no—
327C22×Q8—24no—
328C22×Q8—42no—
329C22×Q8—42no—
330C22×Q8—131no—
331C22×Q8C22×D1312yes—
332C22×Q8C22×D1311yescharacteristic
333C22×D4C22⋊D1311yescharacteristic
334C23×C4—22no—
335C23×C4C22×D1312yes—
336C2×Q16—134no—
337C2×Q16—262no—
338C2×Q16—262no—
339C2×Q16—264no—
340C2×Q16—264no—
341C2×Q16—522no—
342C22×C8—131no—
343C22×C8—132no—
344C22×C8—131no—
345C4⋊Q8—28no—
346C4⋊Q8—22no—
347C4⋊Q8C22⋊D1314yes—
348C22⋊Q8—216no—
349C22⋊Q8—24no—
350C22⋊Q8—24no—
351C22⋊Q8—264no—
352C22⋊Q8—522no—
353C4×Q8—22no—
354C4×Q8—262no—
355C4×Q8—262no—
356C4×Q8C22⋊D1314yes—
357C4×D4—28no—
358C4×D4—22no—
359C4×D4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—132no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4C22⋊D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C22⋊C4—22no—
371C2×C22⋊C4—262no—
372C2×C22⋊C4—262no—
373C2×C22⋊C4C22⋊D1312yes—
374C2×C42—21no—
375C2×C42—261no—
376C2×C42C22×D1311yescharacteristic
377#106—262no—
378C4⋊C8—262no—
379#103—264no—
380#103—264no—
381#103—262no—
382#103—264no—
383#103—262no—
384#103—522no—
385C22⋊C8—264no—
386C22⋊C8—522no—
387#97—262no—
388#95—262no—
389#95—261no—
390#95—261no—
391C2×C13—44no—
392C2×C13#240811yescharacteristic
393C2×C13#300411yescharacteristic
394C2×C13#301111yescharacteristic
395C2×C13#327012yes—
396C2×C13#331212yes—
397C24C2×C22⋊D1312yes—
398C2×Q8—28no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—44no—
408C2×Q8—44no—
409C2×Q8—48no—
410C2×Q8—48no—
411C2×Q8—48no—
412C2×Q8—48no—
413C2×Q8—132no—
414C2×Q8—261no—
415C2×Q8—261no—
416C2×Q8—261no—
417C2×Q8—261no—
418C2×Q8—261no—
419C2×Q8D4×D1312yes—
420C2×Q8#612912yes—
421C2×Q8C2×C22⋊D1314yes—
422C2×Q8C2×C22⋊D1312yes—
423C2×D4—24no—
424C2×D4—22no—
425C22×C4—21no—
426C22×C4—28no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—261no—
438C22×C4—262no—
439C22×C4—261no—
440C22×C4C2×C22⋊D1312yes—
441C22×C4C2×C22⋊D1311yescharacteristic
442C22×C4C2×C22⋊D1311yescharacteristic
443C22×C4C23×D1311yescharacteristic
444Q16—268no—
445Q16—528no—
446C2×C8—132no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—262no—
450C2×C8—261no—
451C2×C8—262no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—262no—
455C4⋊C4—28no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—262no—
462C4⋊C4—262no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—524no—
466C4⋊C4—522no—
467C4⋊C4C2×C22⋊D1312yes—
468C22⋊C4—28no—
469C22⋊C4—24no—
470C22⋊C4—524no—
471C22⋊C4—524no—
472C42—24no—
473C42—522no—
474C42C2×C22⋊D1312yes—
475C42C2×C22⋊D1312yes—
476C13#2425511yescharacteristic, complemented, Sylow
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23#8819614yes—
484C23C22×C22⋊D1311yescharacteristic
485Q8—22no—
486Q8—22no—
487Q8—22no—
488Q8—24no—
489Q8—24no—
490Q8—416no—
491Q8—42no—
492Q8—42no—
493Q8—262no—
494Q8—262no—
495Q8—521no—
496Q8—521no—
497Q8#8819214yes—
498D4—28no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—416no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—262no—
518C2×C4—521no—
519C2×C4—521no—
520C2×C4—522no—
521C2×C4—522no—
522C2×C4—522no—
523C2×C4—522no—
524C2×C4—521no—
525C2×C4#8820712yes—
526C2×C4#8820712yes—
527C2×C4C2×D4×D1311yescharacteristic
528C2×C4C2×#612911yescharacteristic
529C2×C4#8825111yescharacteristic
530C2×C4#8825111yescharacteristic
531C2×C4C22×C22⋊D1311yescharacteristic
532C2×C4C22×C22⋊D1311yescharacteristic
533C8—262no—
534C8—522no—
535C8—521no—
536C22—24no—
537C22—24no—
538C22—24no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22D4×C22⋊D1311yescharacteristic
544C22#1171951111yescharacteristic
545C22C2×#8819612yes—
546C22#1171954312yes—
547C22C2×#8820711yescharacteristic
548C4—22no—
549C4—22no—
550C4—24no—
551C4—42no—
552C4—42no—
553C4—44no—
554C4—522no—
555C4—1042no—
556C4—1041no—
557C4C2×#8819211yescharacteristic
558C4D4×C22⋊D1311yescharacteristic
559C4#1171951011yescharacteristic
560C4#1171951111yescharacteristic
561C2—44no—
562C2#1311818611yescharacteristic
563C2#1312407011yescharacteristic
564C2#1312413111yescharacteristic
565C2#1312640712yes—
566C2#1312688712yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×D4×Q8×C13C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterC2×D4×Q8D13
hypocenterC13#24255
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11718751C2semidirect
2. C2×#11718889C2semidirect
3. C2×#11718691C2semidirect
5. #13116029C2semidirect
6. #13115844C2semidirect
7. #13115657C2semidirect
9. #13114851C2semidirect
10. #13114771C2semidirect
87. C2×#6107D4semidirect
476. C13#24255semidirect

Maximal subgroups

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

subgroupindex
C2×#117187512
C2×#117188892
C2×#117186912
#131197452
#131160292
#131158442
#131156572
#131156352
#131148512
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