Finite Group Databasebeta

← #16794653

Subgroups — #16794653

Order 3328.

1018 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719125C211yesmaximal, characteristic
2C2×#11719129C211yesmaximal, characteristic
3#13130354C214yesmaximal, complemented
4#13130351C212yesmaximal, complemented
5#13130349C212yesmaximal, complemented
6#13130338C214yesmaximal, complemented
7C2×#11719327C211yesmaximal, characteristic
8C22×#6122—21no—
9C2×C13×C22⋊Q8C411yescharacteristic
10C2×Q8×Dic13C411yescharacteristic
11C2×#88198C2211yescharacteristic
12C2×#88178C411yescharacteristic
13C22×C4×Dic13C2211yescharacteristic
14#11719327—21no—
15#11719327—21no—
16#11719327—21no—
17#11719327—21no—
18#11719327C412yes—
19#11719327C412yes—
20#11719327C2212yes—
21#11719327C2212yes—
22C2×#88143—21no—
23C2×#88142C2211yescharacteristic
24C2×#88141—21no—
25C2×#88141C411yescharacteristic
26C2×#88132—21no—
27C2×#88131—21no—
28C2×C22⋊#1057—21no—
29#11719129—21no—
30#11719129—21no—
31#11719129C2212yes—
32#11719129C2212yes—
33#11719125—21no—
34#11719125—21no—
35#11719125C2212yes—
36#11719125C2212yes—
37C2×#88112C2212yes—
38C2×#88112C2212yes—
39C2×C4⋊#1057—21no—
40C2×C4×#1057—21no—
41#11718303C2218yescomplemented
42#11718245C2218yescomplemented
43C22×Q8×C13C2×C411yescharacteristic
44C23×C4×C13C2×C411yescharacteristic
45C23×Dic13D411yescharacteristic
46C23×Dic13D411yescharacteristic
47C22×Dic26—21no—
48C22×Dic26C2×C411yescharacteristic
49C2×#6122—22no—
50C2×#6122—22no—
51C2×#6122—44no—
52C22×#1057—22no—
53C22×#1057—22no—
54C13×C22⋊Q8—21no—
55C13×C22⋊Q8—21no—
56C13×C22⋊Q8C2×C412yes—
57C13×C22⋊Q8C2×C412yes—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4C2×C411yescharacteristic
60C2×C13×C22⋊C4—21no—
61C2×C22⋊Dic13—21no—
62Q8×Dic13—21no—
63Q8×Dic13—21no—
64Q8×Dic13C2×C412yes—
65Q8×Dic13C2×C412yes—
66#88198—21no—
67#88198—21no—
68#88198C2×C412yes—
69#88198C2312yes—
70C2×C4⋊Dic13—21no—
71C2×C4⋊Dic13C2×C411yescharacteristic
72#88178—21no—
73#88178—21no—
74#88178C2×C412yes—
75#88178C2×C412yes—
76C2×#6101—21no—
77C2×#6101—21no—
78C2×#6101—21no—
79C2×#6101—21no—
80C2×#6101—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13—21no—
83C2×C4×Dic13C2×C411yescharacteristic
84C2×C4×Dic13C2×C411yescharacteristic
85C2×C4×Dic13C2×C411yescharacteristic
86C2×C4×Dic13D411yescharacteristic
87C2×C4×Dic13D411yescharacteristic
88C2×C4×Dic13D411yescharacteristic
89C2×C4×Dic13D411yescharacteristic
90C2×C4×Dic13D411yescharacteristic
91C2×C4×Dic13D411yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95#88143—22no—
96#88143—22no—
97#88143—22no—
98#88143—22no—
99#88142—21no—
100#88142—21no—
101#88142C2×C412yes—
102#88142C2312yes—
103#88141—22no—
104#88141—22no—
105#88141—21no—
106#88141—21no—
107#88141—22no—
108#88141—22no—
109#88141C2×C412yes—
110#88141C2×C412yes—
111#88132—22no—
112#88132—22no—
113#88132—22no—
114#88132—22no—
115#88131—22no—
116#88131—22no—
117#88131—22no—
118#88131—22no—
119C22⋊#1057—22no—
120C22⋊#1057—22no—
121#88112—22no—
122#88112—22no—
123#88112C2314yes—
124#88112C2314yes—
125C4⋊#1057—22no—
126C4⋊#1057—22no—
127C4×#1057—22no—
128C4×#1057—22no—
129#17708—131nomaximal, Sylow
130C24×C13C22⋊C411yescharacteristic
131C2×Q8×C13—21no—
132C2×Q8×C13—42no—
133C2×Q8×C13C22×C412yes—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—42no—
137C22×C4×C13C22⋊C411yescharacteristic
138C22×C4×C13C22⋊C411yescharacteristic
139C22×C4×C13C22⋊C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C22×C411yescharacteristic
142C22×C4×C13C22×C411yescharacteristic
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—42no—
146C22×Dic13C22⋊C411yescharacteristic
147C22×Dic13C22⋊C411yescharacteristic
148C22×Dic13C22⋊C411yescharacteristic
149C22×Dic13C22⋊C411yescharacteristic
150C22×Dic13C22⋊C411yescharacteristic
151C22×Dic13C22⋊C411yescharacteristic
152C22×Dic13SD1614yes—
153C22×Dic13Q1614yes—
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C22×Dic13C2×D411yescharacteristic
157C22×Dic13C2×D411yescharacteristic
158C22×Dic13C2×D411yescharacteristic
159C22×Dic13C2×D411yescharacteristic
160C2×Dic26—21no—
161C2×Dic26—22no—
162C2×Dic26—22no—
163C2×Dic26—44no—
164C2×Dic26—42no—
165C2×Dic26C22×C412yes—
166#6122—44no—
167#6122—44no—
168C2×#1057—24no—
169C2×#1057—24no—
170C2×#1057—44no—
171C2×#1057—44no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4C22×C412yes—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—22no—
178C22⋊Dic13—22no—
179C22⋊Dic13—22no—
180C4⋊Dic13—21no—
181C4⋊Dic13—22no—
182C4⋊Dic13—22no—
183C4⋊Dic13C22×C412yes—
184#6101—22no—
185#6101—22no—
186#6101—22no—
187#6101—22no—
188#6101—22no—
189#6101—22no—
190#6101—22no—
191#6101—22no—
192#6101—22no—
193#6101—22no—
194C4×Dic13—22no—
195C4×Dic13—22no—
196C4×Dic13—22no—
197C4×Dic13—22no—
198C4×Dic13C22⋊C411yescharacteristic
199C4×Dic13C22⋊C411yescharacteristic
200C4×Dic13C22⋊C411yescharacteristic
201C4×Dic13C22⋊C411yescharacteristic
202C4×Dic13C22⋊C411yescharacteristic
203C4×Dic13C22⋊C411yescharacteristic
204C4×Dic13C22×C411yescharacteristic
205C4×Dic13C22×C411yescharacteristic
206C4×Dic13C22×C411yescharacteristic
207C4×Dic13C2×D411yescharacteristic
208C4×Dic13C2×D411yescharacteristic
209C4×Dic13C2×D411yescharacteristic
210C4×Dic13C2×D411yescharacteristic
211C4×Dic13C2×D411yescharacteristic
212C4×Dic13C2×D411yescharacteristic
213C4×Dic13C2411yescharacteristic
214C2×#533—131no—
215C2×#431—131no—
216C2×#423—131no—
217#1550—134no—
218#1549—132no—
219#1548—132no—
220#1542—134no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13#10314yes—
224C23×C13C2×C22⋊C411yescharacteristic
225C23×C13C2×C22⋊C411yescharacteristic
226C23×C13C2×C22⋊C411yescharacteristic
227Q8×C13—42no—
228Q8×C13—42no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13C2×C22⋊C411yescharacteristic
240C2×C4×C13C2×C22⋊C411yescharacteristic
241C2×C4×C13C2×C22⋊C411yescharacteristic
242C2×C4×C13C23×C411yescharacteristic
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13#10314yes—
254C2×Dic13#10314yes—
255C2×Dic13#10314yes—
256C2×Dic13C2×C22⋊C411yescharacteristic
257C2×Dic13C2×C22⋊C411yescharacteristic
258C2×Dic13C2×C22⋊C411yescharacteristic
259C2×Dic13C2×C22⋊C411yescharacteristic
260C2×Dic13C2×C22⋊C411yescharacteristic
261C2×Dic13C2×C22⋊C411yescharacteristic
262C2×Dic13C2×SD1612yes—
263C2×Dic13C2×SD1612yes—
264C2×Dic13C2×SD1612yes—
265C2×Dic13C2×Q1612yes—
266C2×Dic13C2×Q1612yes—
267C2×Dic13C2×Q1612yes—
268C2×Dic13C22×D411yescharacteristic
269C2×Dic13C22×D411yescharacteristic
270Dic26—44no—
271Dic26—42no—
272Dic26—44no—
273Dic26—42no—
274#1057—44no—
275#1057—44no—
276C22×M16—261no—
277#533—132no—
278#533—132no—
279#533—132no—
280#533—132no—
281#533—261no—
282#533—261no—
283#533—261no—
284#533—261no—
285C2×C4⋊Q8—131no—
286C2×C4⋊Q8—131no—
287C2×#125—261no—
288C2×C22⋊Q8—131no—
289C2×C22⋊Q8—261no—
290C2×C22⋊Q8#26111yescharacteristic
291C2×C4×Q8—131no—
292C2×C4×Q8—131no—
293C2×C4×Q8—261no—
294C2×#117—261no—
295C22×C42—131no—
296#431—132no—
297#431—132no—
298#431—261no—
299#431—261no—
300#423—132no—
301#423—132no—
302#423—261no—
303#423—261no—
304C2×C4⋊C8—132no—
305C2×C4⋊C8—132no—
306C2×C4⋊C8—261no—
307C2×C22⋊C8—261no—
308C2×C4×C8—261no—
309#333—138no—
310#332—138no—
311C22×C13—21no—
312C22×C13—21no—
313C22×C13—21no—
314C22×C13—21no—
315C22×C13—21no—
316C22×C13—21no—
317C22×C13—44no—
318C22×C13C2×#10312yes—
319C22×C13C2×#10312yes—
320C22×C13C2×#10312yes—
321C22×C13C22×C22⋊C411yescharacteristic
322C4×C13—21no—
323C4×C13—21no—
324C4×C13—21no—
325C4×C13—42no—
326C4×C13—42no—
327C4×C13#41312yes—
328Dic13—21no—
329Dic13—21no—
330Dic13—21no—
331Dic13—42no—
332Dic13—42no—
333Dic13C2×#10312yes—
334Dic13C2×#10312yes—
335Dic13C2×#10312yes—
336Dic13C22×SD1611yescharacteristic
337Dic13C22×Q1611yescharacteristic
338Dic13#57512yes—
339C22×Q8—131no—
340C22×Q8—261no—
341C22×Q8C2×#26111yescharacteristic
342C23×C4—131no—
343C23×C4—131no—
344C23×C4C2×#26111yescharacteristic
345C2×M16—262no—
346C2×M16—262no—
347C2×M16—524no—
348C22×C8—262no—
349C22×C8—262no—
350C4⋊Q8—132no—
351C4⋊Q8—132no—
352C4⋊Q8—132no—
353C4⋊Q8—132no—
354C4⋊Q8—261no—
355C4⋊Q8—261no—
356C4⋊Q8—261no—
357C4⋊Q8—261no—
358#125—262no—
359#125—262no—
360#125—262no—
361#125—262no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—132no—
365C22⋊Q8—132no—
366C22⋊Q8—262no—
367C22⋊Q8—262no—
368C22⋊Q8—262no—
369C22⋊Q8—262no—
370C22⋊Q8—261no—
371C22⋊Q8—261no—
372C22⋊Q8C2×#26112yes—
373C22⋊Q8C2×#26112yes—
374C4×Q8—132no—
375C4×Q8—132no—
376C4×Q8—132no—
377C4×Q8—132no—
378C4×Q8—261no—
379C4×Q8—261no—
380C4×Q8—262no—
381C4×Q8—262no—
382C4×Q8—262no—
383C4×Q8—262no—
384C4×Q8—261no—
385C4×Q8—261no—
386#117—262no—
387#117—262no—
388#117—262no—
389#117—262no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4C2×#26111yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—261no—
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—131no—
404C2×C42—131no—
405C2×C42—131no—
406C2×C42—131no—
407C2×C42—131no—
408C2×C42—131no—
409C2×C42—131no—
410C2×C42—131no—
411C2×C42—131no—
412C2×C42—131no—
413C2×C42—261no—
414C2×C42—261no—
415C4⋊C8—134no—
416C4⋊C8—134no—
417C4⋊C8—262no—
418C4⋊C8—262no—
419C4⋊C8—262no—
420C4⋊C8—262no—
421C22⋊C8—262no—
422C22⋊C8—262no—
423C4×C8—262no—
424C4×C8—262no—
425C2×C13—22no—
426C2×C13—22no—
427C2×C13—22no—
428C2×C13C2×#41311yescharacteristic
429C2×C13C22×#10311yescharacteristic
430C2×C13#289611yescharacteristic
431C24C22⋊#26111yescharacteristic
432C2×Q8—21no—
433C2×Q8—42no—
434C2×Q8—132no—
435C2×Q8—262no—
436C2×Q8—262no—
437C2×Q8—261no—
438C2×Q8—522no—
439C2×Q8—524no—
440C2×Q8C22×#26112yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—42no—
444C22×C4—134no—
445C22×C4—134no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—522no—
461C22×C4C22⋊#26111yescharacteristic
462C22×C4C22⋊#26111yescharacteristic
463C22×C4C22⋊#26111yescharacteristic
464C22×C4C22×#26111yescharacteristic
465C22×C4C22×#26111yescharacteristic
466C22×C4C22×#26111yescharacteristic
467M16—524no—
468M16—524no—
469C2×C8—264no—
470C2×C8—264no—
471C2×C8—524no—
472C2×C8—524no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—132no—
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—
486C4⋊C4—262no—
487C4⋊C4—261no—
488C4⋊C4—262no—
489C4⋊C4—262no—
490C4⋊C4C22×#26112yes—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—262no—
494C22⋊C4—262no—
495C42—131no—
496C42—131no—
497C42—131no—
498C42—131no—
499C42—131no—
500C42—131no—
501C42—131no—
502C42—131no—
503C42—131no—
504C42—131no—
505C42—131no—
506C42—131no—
507C42—131no—
508C42—131no—
509C42—131no—
510C42—131no—
511C42—262no—
512C42—262no—
513C42—262no—
514C42—262no—
515C13#1770811yescharacteristic, complemented, Sylow
516C23—41no—
517C23—41no—
518C23#8811714yes—
519C23C2×C22⋊#26111yescharacteristic
520C23C2×C22⋊#26111yescharacteristic
521C23C2×C22⋊#26111yescharacteristic
522Q8—42no—
523Q8—42no—
524Q8—522no—
525Q8—524no—
526Q8—524no—
527Q8—522no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—131no—
539C2×C4—131no—
540C2×C4—131no—
541C2×C4—131no—
542C2×C4—131no—
543C2×C4—132no—
544C2×C4—132no—
545C2×C4—132no—
546C2×C4—134no—
547C2×C4—134no—
548C2×C4—134no—
549C2×C4—132no—
550C2×C4—132no—
551C2×C4—132no—
552C2×C4—131no—
553C2×C4—131no—
554C2×C4—131no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—262no—
558C2×C4—262no—
559C2×C4—262no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4C2×C22⋊#26111yescharacteristic
566C2×C4C2×C22⋊#26111yescharacteristic
567C2×C4C2×C22⋊#26111yescharacteristic
568C2×C4C23×#26111yescharacteristic
569C8—524no—
570C8—524no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—44no—
578C22C2×#8811712yes—
579C22C2×#8811712yes—
580C22C2×#8811712yes—
581C22C22×C22⋊#26111yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—42no—
586C4—42no—
587C4—131no—
588C4—131no—
589C4—132no—
590C4—132no—
591C4—132no—
592C4—132no—
593C4—261no—
594C4—261no—
595C4—261no—
596C4—522no—
597C4—522no—
598C4#1171914812yes—
599C2—22no—
600C2—22no—
601C2—22no—
602C2C2×#1171914811yescharacteristic
603C2C22×#8811711yescharacteristic
604C2#1313145611yescharacteristic
subgroupG/H
centerC22C22×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×C22⋊Q8C4
socleC22×C13C22×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC4×Dic13C24
hypercenterC2×C22⋊Q8#261
hypocenterC13#17708
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13130354C2semidirect
4. #13130351C2semidirect
5. #13130349C2semidirect
6. #13130338C2semidirect
41. #11718303C22semidirect
42. #11718245C22semidirect
515. C13#17708semidirect

Maximal subgroups

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

subgroupindex
C2×#117191252
C2×#117191292
#131303542
#131303512
#131303492
#131303382
C2×#117193272
#1770813