Finite Group Databasebeta

← C2×#13131030 #16799406

Subgroups — C2×#13131030 #16799406

Order 3328.

1126 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719129C211yesmaximal, characteristic
2C2×C4×#6122C211yesmaximal, characteristic
3#13131030C218yesmaximal, direct product factor
4C2×#11718291C212yesmaximal
5C2×#11718291C212yesmaximal
6C22×#88143C211yesmaximal, characteristic
7C22×#6122C2212yes—
8C22×#6122C2212yes—
9C22×C13×C4⋊C4C411yescharacteristic
10C22×C4⋊Dic13C411yescharacteristic
11C22×#6101C411yescharacteristic
12C22×#6101C411yescharacteristic
13C22×#6101C2211yescharacteristic
14C22×#6101C2211yescharacteristic
15C22×C4×Dic13C2211yescharacteristic
16C2×#88143—21no—
17C2×#88143—21no—
18C2×#88143—21no—
19C2×#88143—22no—
20C2×#88143—21no—
21C2×#88143—22no—
22C2×#88143C414yes—
23C2×#88143C2214yes—
24#11719129—22no—
25#11719129C2214yes—
26C2×#88112—21no—
27C4×#6122—22no—
28C4×#6122C2214yes—
29C2×#88110—21no—
30C2×C4⋊#1057—21no—
31C2×C4×#1057—21no—
32#11718291C2218yes—
33#11718291C2218yes—
34C23×C4×C13C2×C411yescharacteristic
35C23×C4×C13C2×C411yescharacteristic
36C23×C4×C13C2×C411yescharacteristic
37C23×Dic13C2×C411yescharacteristic
38C23×Dic13C2×C411yescharacteristic
39C23×Dic13C2×C411yescharacteristic
40C23×Dic13C2311yescharacteristic
41C2×#6122—22no—
42C2×#6122—24no—
43C2×#6122—22no—
44C2×#6122—28no—
45C2×#6122Q818yes—
46C2×#6122C2314yes—
47C2×#6122C2314yes—
48C22×#1057—22no—
49C22×#1057—22no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4C2×C414yes—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13C2×C414yes—
58C2×#6101—21no—
59C2×#6101—21no—
60C2×#6101—22no—
61C2×#6101—21no—
62C2×#6101—21no—
63C2×#6101—22no—
64C2×#6101—21no—
65C2×#6101—21no—
66C2×#6101—21no—
67C2×#6101—21no—
68C2×#6101—21no—
69C2×#6101—21no—
70C2×#6101—21no—
71C2×#6101—21no—
72C2×#6101C2×C412yes—
73C2×#6101C2×C412yes—
74C2×#6101C2×C414yes—
75C2×#6101C2×C414yes—
76C2×#6101C2312yes—
77C2×#6101C2312yes—
78C2×C4×Dic13C2×C412yes—
79C2×C4×Dic13D411yescharacteristic
80C2×C4×Dic13D411yescharacteristic
81C2×C4×Dic13D411yescharacteristic
82C2×C4×Dic13D412yes—
83C2×C4×Dic13D411yescharacteristic
84C2×C4×Dic13D412yes—
85C2×C4×Dic13C2312yes—
86#88143—24no—
87#88143—24no—
88#88143—24no—
89#88143—24no—
90#88143—24no—
91#88143—24no—
92#88143—24no—
93#88143—24no—
94#88112—24no—
95#88110—24no—
96C4⋊#1057—24no—
97C4×#1057—24no—
98C2×#1998—131nomaximal, Sylow
99C24×C13C22×C411yescharacteristic
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—42no—
105C22×C4×C13—42no—
106C22×C4×C13—42no—
107C22×C4×C13C22⋊C411yescharacteristic
108C22×C4×C13C22⋊C411yescharacteristic
109C22×C4×C13C22⋊C412yes—
110C22×C4×C13C22×C412yes—
111C22×C4×C13C22×C412yes—
112C22×C4×C13C22×C412yes—
113C22×Dic13—21no—
114C22×Dic13—21no—
115C22×Dic13—21no—
116C22×Dic13—21no—
117C22×Dic13—42no—
118C22×Dic13—42no—
119C22×Dic13—42no—
120C22×Dic13C22⋊C411yescharacteristic
121C22×Dic13C22⋊C411yescharacteristic
122C22×Dic13C22⋊C412yes—
123C22×Dic13C22×C412yes—
124C22×Dic13C22×C412yes—
125C22×Dic13C22×C412yes—
126C22×Dic13C22×C411yescharacteristic
127C22×Dic13C2×D411yescharacteristic
128C22×Dic13C2×D411yescharacteristic
129C22×Dic13C2×D411yescharacteristic
130C22×Dic13C2×D411yescharacteristic
131C22×Dic13C2×Q814yes—
132C22×Dic13#4114yes—
133C22×Dic13C2411yescharacteristic
134#6122—28no—
135#6122—24no—
136#6122—28no—
137#6122—44no—
138#6122C2×Q818yes—
139C2×#1057—28no—
140C2×#1057—24no—
141C2×#1057—24no—
142C2×#1057—44no—
143C13×C4⋊C4—24no—
144C13×C4⋊C4—24no—
145C4⋊Dic13—24no—
146C4⋊Dic13—24no—
147#6101—24no—
148#6101—24no—
149#6101—24no—
150#6101—24no—
151#6101—22no—
152#6101—22no—
153#6101—22no—
154#6101—22no—
155#6101—22no—
156#6101—22no—
157#6101—22no—
158#6101—22no—
159C4×Dic13C22⋊C412yes—
160C4×Dic13C22⋊C412yes—
161C4×Dic13C22⋊C412yes—
162C4×Dic13C22⋊C412yes—
163C4×Dic13C2×D412yes—
164C4×Dic13C2×D412yes—
165C4×Dic13C2×D412yes—
166C4×Dic13C2×D412yes—
167C22×#125—131no—
168C2×#423—131no—
169C2×C4×M16—131no—
170#1998—138no—
171C2×#343—132no—
172C2×#343—132no—
173C23×C13—22no—
174C23×C13—22no—
175C23×C13C2×C22⋊C411yescharacteristic
176C23×C13C2×C22⋊C411yescharacteristic
177C23×C13C4×Q814yes—
178C23×C13C23×C411yescharacteristic
179C2×C4×C13—22no—
180C2×C4×C13—22no—
181C2×C4×C13—22no—
182C2×C4×C13—22no—
183C2×C4×C13—42no—
184C2×C4×C13—42no—
185C2×C4×C13—42no—
186C2×C4×C13—42no—
187C2×C4×C13—42no—
188C2×C4×C13—42no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13C2×C22⋊C412yes—
192C2×C4×C13C2×C22⋊C412yes—
193C2×Dic13—22no—
194C2×Dic13—22no—
195C2×Dic13—22no—
196C2×Dic13—22no—
197C2×Dic13—42no—
198C2×Dic13—42no—
199C2×Dic13—42no—
200C2×Dic13—42no—
201C2×Dic13—42no—
202C2×Dic13—42no—
203C2×Dic13—42no—
204C2×Dic13—42no—
205C2×Dic13C2×C22⋊C412yes—
206C2×Dic13C2×C22⋊C412yes—
207C2×Dic13C2×C22⋊C411yescharacteristic
208C2×Dic13C2×C22⋊C411yescharacteristic
209C2×Dic13C4×Q814yes—
210C2×Dic13C22⋊Q814yes—
211C2×Dic13C22⋊Q814yes—
212C2×Dic13#12412yes—
213C2×Dic13#12412yes—
214C2×Dic13C4⋊Q812yes—
215C2×Dic13C4⋊Q812yes—
216C2×Dic13C22×D411yescharacteristic
217C2×Dic13C22×D411yescharacteristic
218C2×Dic13C22×Q812yes—
219C2×Dic13C2×#4112yes—
220#1057—28no—
221#1057—44no—
222C22×M16—132no—
223C22×M16—132no—
224C2×#125—134no—
225C2×#125—134no—
226C2×#125—261no—
227C2×#125—261no—
228C2×#125—262no—
229C2×#125—261no—
230C2×#125—261no—
231C2×#125—262no—
232C22×C4⋊C4—131no—
233C22×C4⋊C4—131no—
234C22×C4⋊C4—131no—
235C22×C4⋊C4—131no—
236C22×C4⋊C4—131no—
237C22×C4⋊C4#26111yescharacteristic
238C22×C42—131no—
239#423—134no—
240#423—262no—
241C2×C4⋊C8—261no—
242C2×C4⋊C8—261no—
243C4×M16—134no—
244C4×M16—262no—
245C2×#97—261no—
246C2×C4×C8—261no—
247#343—138no—
248#343—138no—
249C22×C13—21no—
250C22×C13—21no—
251C22×C13—21no—
252C22×C13—21no—
253C22×C13—28no—
254C22×C13#39112yes—
255C22×C13#39112yes—
256C22×C13#41312yes—
257C22×C13#41312yes—
258C22×C13C22×C22⋊C411yescharacteristic
259C22×C13C2×C4×Q812yes—
260C4×C13—22no—
261C4×C13—22no—
262C4×C13—42no—
263C4×C13—42no—
264Dic13—22no—
265Dic13—22no—
266Dic13—42no—
267Dic13—42no—
268Dic13#39112yes—
269Dic13#39112yes—
270Dic13C2×C22⋊Q812yes—
271Dic13C2×#12411yescharacteristic
272Dic13C2×C4⋊Q811yescharacteristic
273C23×C4—131no—
274C23×C4—131no—
275C23×C4—131no—
276C23×C4—131no—
277C23×C4C2×#26111yescharacteristic
278C23×C4C2×#26111yescharacteristic
279C23×C4C2×#26111yescharacteristic
280C2×M16—134no—
281C2×M16—138no—
282C2×M16—134no—
283C2×M16—262no—
284C2×M16—264no—
285C2×M16—262no—
286C2×M16—268no—
287C22×C8—262no—
288C22×C8—262no—
289#125—264no—
290#125—264no—
291#125—264no—
292#125—264no—
293#125—264no—
294#125—264no—
295#125—264no—
296#125—264no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—132no—
301C2×C4⋊C4—132no—
302C2×C4⋊C4—132no—
303C2×C4⋊C4—132no—
304C2×C4⋊C4—134no—
305C2×C4⋊C4—134no—
306C2×C4⋊C4—134no—
307C2×C4⋊C4—261no—
308C2×C4⋊C4—261no—
309C2×C4⋊C4—261no—
310C2×C4⋊C4—261no—
311C2×C4⋊C4—262no—
312C2×C4⋊C4—261no—
313C2×C4⋊C4—261no—
314C2×C4⋊C4—261no—
315C2×C4⋊C4—261no—
316C2×C4⋊C4—261no—
317C2×C4⋊C4—261no—
318C2×C4⋊C4—262no—
319C2×C4⋊C4—261no—
320C2×C4⋊C4—261no—
321C2×C4⋊C4—262no—
322C2×C4⋊C4—261no—
323C2×C4⋊C4—261no—
324C2×C4⋊C4C2×#26114yes—
325C2×C42—131no—
326C2×C42—131no—
327C2×C42—132no—
328C2×C42—131no—
329C2×C42—131no—
330C2×C42—132no—
331C2×C42—132no—
332C2×C42—132no—
333C4⋊C8—264no—
334C4⋊C8—264no—
335#97—264no—
336C4×C8—264no—
337C2×C13—22no—
338C2×C13—22no—
339C2×C13#199814yescomplemented
340C2×C13C2×#39111yescharacteristic
341C2×C13C2×#41311yescharacteristic
342C2×C13C2×#41311yescharacteristic
343C24C22×#26111yescharacteristic
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—134no—
352C22×C4—134no—
353C22×C4—131no—
354C22×C4—131no—
355C22×C4—131no—
356C22×C4—131no—
357C22×C4—131no—
358C22×C4—131no—
359C22×C4—131no—
360C22×C4—131no—
361C22×C4—132no—
362C22×C4—132no—
363C22×C4—132no—
364C22×C4—132no—
365C22×C4—261no—
366C22×C4—261no—
367C22×C4—261no—
368C22×C4—261no—
369C22×C4—522no—
370C22×C4—522no—
371C22×C4—522no—
372C22×C4C22⋊#26111yescharacteristic
373C22×C4C22⋊#26111yescharacteristic
374C22×C4C22⋊#26112yes—
375C22×C4C22×#26112yes—
376C22×C4C22×#26112yes—
377C22×C4C22×#26112yes—
378M16—138no—
379M16—264no—
380M16—268no—
381M16—268no—
382M16—524no—
383C2×C8—264no—
384C2×C8—268no—
385C2×C8—264no—
386C2×C8—524no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—262no—
390C4⋊C4—262no—
391C4⋊C4—262no—
392C4⋊C4—262no—
393C4⋊C4—262no—
394C4⋊C4—262no—
395C4⋊C4—262no—
396C4⋊C4—262no—
397C4⋊C4—264no—
398C4⋊C4—264no—
399C4⋊C4—264no—
400C4⋊C4—264no—
401C4⋊C4—264no—
402C4⋊C4—264no—
403C42—132no—
404C42—132no—
405C42—132no—
406C42—132no—
407C42—132no—
408C42—132no—
409C42—132no—
410C42—132no—
411C13C2×#199811yescharacteristic, complemented, Sylow
412C23—22no—
413C23—22no—
414C23Q8×#26114yes—
415C23C2×C22⋊#26111yescharacteristic
416C23C2×C22⋊#26111yescharacteristic
417C23C23×#26111yescharacteristic
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—132no—
431C2×C4—132no—
432C2×C4—134no—
433C2×C4—131no—
434C2×C4—131no—
435C2×C4—131no—
436C2×C4—131no—
437C2×C4—134no—
438C2×C4—132no—
439C2×C4—134no—
440C2×C4—132no—
441C2×C4—132no—
442C2×C4—132no—
443C2×C4—132no—
444C2×C4—132no—
445C2×C4—262no—
446C2×C4—262no—
447C2×C4—262no—
448C2×C4—262no—
449C2×C4—522no—
450C2×C4—522no—
451C2×C4—522no—
452C2×C4—522no—
453C2×C4—522no—
454C2×C4—522no—
455C2×C4—522no—
456C2×C4—522no—
457C2×C4C2×C22⋊#26112yes—
458C2×C4C2×C22⋊#26112yes—
459C8—268no—
460C8—524no—
461C22—28no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22#1171913212yes—
467C22#1171914812yes—
468C22(C2×#261)⋊Q812yes—
469C22(C2×#261)⋊Q812yes—
470C22C2×Q8×#26112yes—
471C22C22×C22⋊#26111yescharacteristic
472C4—22no—
473C4—22no—
474C4—42no—
475C4—42no—
476C4—132no—
477C4—131no—
478C4—131no—
479C4—132no—
480C4—132no—
481C4—262no—
482C4—262no—
483C4—522no—
484C4—522no—
485C2—22no—
486C2—22no—
487C2#1313103014yesdirect product factor
488C2C2×(C2×#261)⋊Q811yescharacteristic
489C2C2×#1171913211yescharacteristic
490C2C2×#1171914811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenterC22×C4⋊C4#261
hypocenterC13C2×#1998
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13131030C2direct (N × H)
339. C2×C13#1998semidirect
411. C13C2×#1998semidirect
487. C2#13131030direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191292
C2×C4×#61222
#131310302
C2×#117182912
C22×#881432
C2×#199813