Finite Group Databasebeta

← C2×#13130139 #16793296

Subgroups — C2×#13130139 #16793296

Order 3328.

1282 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719051C211yesmaximal, characteristic
2C2×#11719049C211yesmaximal, characteristic
3#13130139C218yesmaximal, direct product factor
4C2×#11718244C212yesmaximal, complemented
5C2×Q8⋊#1057C212yesmaximal, complemented
6C2×C4×Q8×D13C211yesmaximal, characteristic
7C22×Q8×D13C411yescharacteristic
8C2×C4×Q8×C13C411yescharacteristic
9C2×Q8×Dic13C2211yescharacteristic
10C4×Q8×D13—22no—
11C4×Q8×D13—22no—
12C4×Q8×D13C414yes—
13C4×Q8×D13C2214yes—
14C2×C4⋊C4×D13—21no—
15C2×C4⋊C4×D13C411yescharacteristic
16C2×#88141—21no—
17C2×#88141C2211yescharacteristic
18C2×C42×D13—21no—
19C2×C42×D13C2211yescharacteristic
20C2×C4×Dic26—21no—
21C2×C4×Dic26C411yescharacteristic
22C2×#88112—21no—
23C2×#88111—21no—
24C2×#88111—21no—
25C2×C4⋊#1057C2212yes—
26C2×C4×#1057—21no—
27C2×C4×#1057C2212yes—
28#11719051—22no—
29#11719051C2214yes—
30#11719049—22no—
31#11719049C2214yes—
32Q8⋊#1057C2218yescomplemented
33#11718244C2218yescomplemented
34C22×Q8×C13C2×C411yescharacteristic
35C2×Q8×D13—22no—
36C2×Q8×D13—24no—
37C2×Q8×D13C818yescomplemented
38C2×Q8×D13C2×C414yes—
39C22×C4×D13—21no—
40C22×C4×D13—21no—
41C22×C4×D13C2×C411yescharacteristic
42C22×C4×D13D411yescharacteristic
43C22×C4×D13D411yescharacteristic
44C22×Dic26—21no—
45C22×Dic26C2×C411yescharacteristic
46C22×#1057—22no—
47C22×#1057—22no—
48C4×Q8×C13—22no—
49C4×Q8×C13C2×C414yes—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4C2×C411yescharacteristic
52C2×C42×C13—21no—
53C2×C42×C13C2×C411yescharacteristic
54Q8×Dic13—21no—
55Q8×Dic13—21no—
56Q8×Dic13C2×C412yes—
57Q8×Dic13C2312yes—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13C2×C411yescharacteristic
60C2×#6101—21no—
61C2×#6101—21no—
62C2×#6101—21no—
63C2×C4×Dic13—21no—
64C2×C4×Dic13—21no—
65C2×C4×Dic13—21no—
66C2×C4×Dic13D411yescharacteristic
67C2×C4×Dic13D411yescharacteristic
68C2×C4×Dic13C2311yescharacteristic
69C4⋊C4×D13—24no—
70C4⋊C4×D13—22no—
71C4⋊C4×D13—24no—
72C4⋊C4×D13C2×C414yes—
73#88141—24no—
74#88141—24no—
75#88141—21no—
76#88141—21no—
77#88141C2×C412yes—
78#88141C2312yes—
79C42×D13—24no—
80C42×D13—24no—
81C42×D13C2×C412yes—
82C42×D13D412yes—
83C42×D13D412yes—
84C42×D13C2312yes—
85C4×Dic26—22no—
86C4×Dic26—24no—
87C4×Dic26—24no—
88C4×Dic26C2×C414yes—
89#88112—24no—
90#88111—24no—
91#88111—24no—
92C4⋊#1057—22no—
93C4⋊#1057C2314yes—
94C4×#1057—22no—
95C4×#1057—24no—
96C4×#1057C2314yes—
97C2×#1479—131nomaximal, Sylow
98C23×D13C22⋊C411yescharacteristic
99C2×Q8×C13—21no—
100C2×Q8×C13—22no—
101C2×Q8×C13C2×C814yes—
102C2×Q8×C13C22×C412yes—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13C22⋊C411yescharacteristic
106C22×C4×C13C22⋊C411yescharacteristic
107C22×C4×C13C22×C411yescharacteristic
108C22×Dic13—21no—
109C22×Dic13—21no—
110C22×Dic13C22⋊C411yescharacteristic
111C22×Dic13C2×D411yescharacteristic
112C22×Dic13C2×D411yescharacteristic
113Q8×D13—216no—
114Q8×D13—28no—
115Q8×D13C2×C8116yescomplemented
116C2×C4×D13—28no—
117C2×C4×D13—24no—
118C2×C4×D13—24no—
119C2×C4×D13—24no—
120C2×C4×D13—42no—
121C2×C4×D13—44no—
122C2×C4×D13C22⋊C412yes—
123C2×C4×D13C22⋊C412yes—
124C2×C4×D13C22⋊C412yes—
125C2×C4×D13C2×C814yes—
126C2×C4×D13M1614yes—
127C2×C4×D13C22×C412yes—
128C2×C4×D13C2×D412yes—
129C2×C4×D13C2×D412yes—
130C2×Dic26—21no—
131C2×Dic26—22no—
132C2×Dic26—28no—
133C2×Dic26—24no—
134C2×Dic26C2×C814yes—
135C2×Dic26C22×C412yes—
136C2×#1057—24no—
137C2×#1057—24no—
138C2×#1057—44no—
139C2×#1057—44no—
140C13×C4⋊C4—24no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4C22×C412yes—
143C42×C13—24no—
144C42×C13C22⋊C412yes—
145C42×C13C22×C412yes—
146C4⋊Dic13—21no—
147C4⋊Dic13—22no—
148C4⋊Dic13—22no—
149C4⋊Dic13C22×C412yes—
150#6101—24no—
151#6101—24no—
152#6101—22no—
153#6101—22no—
154C4×Dic13—24no—
155C4×Dic13—22no—
156C4×Dic13—22no—
157C4×Dic13—22no—
158C4×Dic13—22no—
159C4×Dic13C22⋊C412yes—
160C4×Dic13C22⋊C412yes—
161C4×Dic13C22×C411yescharacteristic
162C4×Dic13C2×D411yescharacteristic
163C4×Dic13C2×D412yes—
164C4×Dic13C2×D411yescharacteristic
165C4×Dic13C2×D412yes—
166C4×Dic13C2411yescharacteristic
167C22×C4×Q8—131no—
168C2×#431—131no—
169C2×#431—131no—
170#1479—138no—
171C2×Q8⋊C8—132no—
172C2×Q8⋊C8—132no—
173C23×C13C2×C22⋊C411yescharacteristic
174C22×D13—22no—
175C22×D13—22no—
176C22×D13C22⋊C814yes—
177C22×D13C2×C22⋊C412yes—
178Q8×C13—22no—
179Q8×C13—24no—
180Q8×C13C22×C814yes—
181C2×C4×C13—22no—
182C2×C4×C13—24no—
183C2×C4×C13—22no—
184C2×C4×C13—22no—
185C2×C4×C13—22no—
186C2×C4×C13—42no—
187C2×C4×C13C2×C22⋊C412yes—
188C2×C4×C13C2×C22⋊C412yes—
189C2×C4×C13C2×C22⋊C411yescharacteristic
190C2×C4×C13C22×C812yes—
191C2×C4×C13C2×M1612yes—
192C2×C4×C13C23×C411yescharacteristic
193C2×Dic13—22no—
194C2×Dic13—24no—
195C2×Dic13—22no—
196C2×Dic13—22no—
197C2×Dic13—42no—
198C2×Dic13C22⋊C814yes—
199C2×Dic13C2×C22⋊C411yescharacteristic
200C2×Dic13C2×C22⋊C412yes—
201C2×Dic13C2×C22⋊C411yescharacteristic
202C2×Dic13#13714yes—
203C2×Dic13C22×D411yescharacteristic
204C2×Dic13C22×D411yescharacteristic
205C4×D13—216no—
206C4×D13—24no—
207C4×D13—24no—
208C4×D13—42no—
209C4×D13—42no—
210C4×D13—48no—
211C4×D13C22⋊C818yes—
212C4×D13C22×C814yes—
213C4×D13C2×M1614yes—
214Dic26—22no—
215Dic26—24no—
216Dic26—216no—
217Dic26C22×C814yes—
218#1057—44no—
219#1057—44no—
220C23×Q8—131no—
221C2×C4×Q8—131no—
222C2×C4×Q8—134no—
223C2×C4×Q8—134no—
224C2×C4×Q8—131no—
225C2×C4×Q8—131no—
226C2×C4×Q8—261no—
227C2×C4×Q8—261no—
228C2×C4×Q8—262no—
229C2×C4×Q8—262no—
230C2×C4×Q8#26111yescharacteristic
231C22×C4⋊C4—131no—
232C22×C4⋊C4—261no—
233C22×C42—131no—
234C22×C42—261no—
235#431—134no—
236#431—134no—
237#431—262no—
238#431—262no—
239C2×C4⋊C8—132no—
240C2×C4⋊C8—261no—
241C2×C22⋊C8—261no—
242C2×C22⋊C8—261no—
243C2×C4×C8—132no—
244C2×C4×C8—261no—
245Q8⋊C8—138no—
246Q8⋊C8—138no—
247C22×C13C2×C22⋊C812yes—
248C22×C13#41912yes—
249C22×C13#42112yes—
250C22×C13C22×C22⋊C411yescharacteristic
251C2×D13—22no—
252C2×D13—22no—
253C2×D13—28no—
254C2×D13C2×C22⋊C814yes—
255C4×C13—24no—
256C4×C13—22no—
257C4×C13—22no—
258C4×C13—42no—
259C4×C13C2×C22⋊C812yes—
260C4×C13C23×C811yescharacteristic
261C4×C13C22×M1611yescharacteristic
262Dic13—24no—
263Dic13—21no—
264Dic13—21no—
265Dic13—42no—
266Dic13C2×C22⋊C814yes—
267Dic13#41912yes—
268Dic13C2×#13712yes—
269C22×Q8—138no—
270C22×Q8—134no—
271C22×Q8—131no—
272C22×Q8—261no—
273C22×Q8—262no—
274C22×Q8—264no—
275C22×Q8C2×#26111yescharacteristic
276C23×C4—131no—
277C23×C4—131no—
278C23×C4—131no—
279C23×C4—261no—
280C23×C4—261no—
281C22×C8—262no—
282C22×C8—262no—
283C4×Q8—22no—
284C4×Q8—132no—
285C4×Q8—132no—
286C4×Q8—132no—
287C4×Q8—132no—
288C4×Q8—134no—
289C4×Q8—264no—
290C4×Q8—264no—
291C4×Q8—264no—
292C4×Q8—261no—
293C4×Q8—261no—
294C4×Q8—264no—
295C4×Q8—261no—
296C4×Q8—261no—
297C4×Q8—262no—
298C4×Q8C2×#26114yes—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—131no—
301C2×C4⋊C4—134no—
302C2×C4⋊C4—262no—
303C2×C4⋊C4—264no—
304C2×C4⋊C4—264no—
305C2×C4⋊C4—261no—
306C2×C4⋊C4—261no—
307C2×C4⋊C4—261no—
308C2×C4⋊C4—261no—
309C2×C4⋊C4C2×#26111yescharacteristic
310C2×C42—21no—
311C2×C42—131no—
312C2×C42—131no—
313C2×C42—131no—
314C2×C42—132no—
315C2×C42—132no—
316C2×C42—132no—
317C2×C42—132no—
318C2×C42—264no—
319C2×C42—264no—
320C2×C42—261no—
321C2×C42—261no—
322C2×C42—261no—
323C2×C42C2×#26111yescharacteristic
324C4⋊C8—134no—
325C4⋊C8—262no—
326C4⋊C8—264no—
327C22⋊C8—264no—
328C22⋊C8—264no—
329C4×C8—134no—
330C4×C8—262no—
331C4×C8—264no—
332C2×C13#147914yescomplemented
333C2×C13C22×C22⋊C811yescharacteristic
334C2×C13C2×#41911yescharacteristic
335C2×C13C2×#42111yescharacteristic
336D13—24no—
337C24—131no—
338C2×Q8—22no—
339C2×Q8—21no—
340C2×Q8—1316no—
341C2×Q8—134no—
342C2×Q8—132no—
343C2×Q8—264no—
344C2×Q8—268no—
345C2×Q8—268no—
346C2×Q8—2616no—
347C2×Q8—262no—
348C2×Q8—261no—
349C2×Q8D13⋊C814yes—
350C2×Q8C22×#26112yes—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—131no—
354C22×C4—131no—
355C22×C4—134no—
356C22×C4—134no—
357C22×C4—132no—
358C22×C4—132no—
359C22×C4—131no—
360C22×C4—132no—
361C22×C4—132no—
362C22×C4—132no—
363C22×C4—132no—
364C22×C4—264no—
365C22×C4—264no—
366C22×C4—268no—
367C22×C4—264no—
368C22×C4—261no—
369C22×C4—261no—
370C22×C4—522no—
371C22×C4—524no—
372C22×C4C22⋊#26111yescharacteristic
373C22×C4C22⋊#26111yescharacteristic
374C22×C4C22×#26111yescharacteristic
375C2×C8—264no—
376C2×C8—264no—
377C2×C8—524no—
378C2×C8—524no—
379C4⋊C4—24no—
380C4⋊C4—21no—
381C4⋊C4—132no—
382C4⋊C4—264no—
383C4⋊C4—262no—
384C4⋊C4—262no—
385C4⋊C4—262no—
386C4⋊C4—262no—
387C4⋊C4—261no—
388C4⋊C4—264no—
389C4⋊C4C22×#26112yes—
390C42—24no—
391C42—132no—
392C42—131no—
393C42—131no—
394C42—132no—
395C42—132no—
396C42—132no—
397C42—131no—
398C42—131no—
399C42—262no—
400C42—262no—
401C42—262no—
402C42—262no—
403C42—264no—
404C42C22⋊#26112yes—
405C42C22×#26112yes—
406C13C2×#147911yescharacteristic, complemented, Sylow
407C23—132no—
408C23—134no—
409C23—262no—
410C23—262no—
411C23C2×C22⋊#26111yescharacteristic
412Q8—22no—
413Q8—24no—
414Q8—134no—
415Q8—2616no—
416Q8—262no—
417Q8—264no—
418Q8C2×D13⋊C814yes—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—42no—
425C2×C4—131no—
426C2×C4—131no—
427C2×C4—132no—
428C2×C4—134no—
429C2×C4—134no—
430C2×C4—134no—
431C2×C4—134no—
432C2×C4—138no—
433C2×C4—131no—
434C2×C4—131no—
435C2×C4—264no—
436C2×C4—264no—
437C2×C4—2616no—
438C2×C4—262no—
439C2×C4—264no—
440C2×C4—262no—
441C2×C4—262no—
442C2×C4—522no—
443C2×C4—522no—
444C2×C4—528no—
445C2×C4—522no—
446C2×C4C2×D13⋊C812yes—
447C2×C4D13⋊M1612yes—
448C2×C4C2×C22⋊#26112yes—
449C2×C4C2×C22⋊#26112yes—
450C2×C4C2×C22⋊#26111yescharacteristic
451C2×C4C23×#26111yescharacteristic
452C8—524no—
453C8—524no—
454C22—134no—
455C22—268no—
456C22—262no—
457C22—262no—
458C22D13⋊(C22⋊C8)12yes—
459C22#1171915312yes—
460C22#1171916612yes—
461C22C22×C22⋊#26111yescharacteristic
462C4—24no—
463C4—22no—
464C4—22no—
465C4—42no—
466C4—134no—
467C4—132no—
468C4—132no—
469C4—264no—
470C4—261no—
471C4—261no—
472C4—522no—
473C4D13⋊(C22⋊C8)12yes—
474C4C22×D13⋊C811yescharacteristic
475C4C2×D13⋊M1611yescharacteristic
476C2—264no—
477C2#1313013914yesdirect product factor
478C2C2×D13⋊(C22⋊C8)11yescharacteristic
479C2C2×#1171915311yescharacteristic
480C2C2×#1171916611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC2×C4×Q8×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC4×Dic13C24
hypercenterC2×C4×Q8#261
hypocenterC13C2×#1479
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #13130139C2direct (N × H)
4. C2×#11718244C2semidirect
5. C2×Q8⋊#1057C2semidirect
32. Q8⋊#1057C22semidirect
33. #11718244C22semidirect
37. C2×Q8×D13C8semidirect
115. Q8×D13C2×C8semidirect
332. C2×C13#1479semidirect
406. C13C2×#1479semidirect
477. C2#13130139direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117190512
C2×#117190492
#131301392
C2×#117182442
C2×Q8⋊#10572
C2×C4×Q8×D132
C2×#147913