Finite Group Databasebeta

← #15919040

Subgroups — #15919040

Order 3328.

1056 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718726C211yesmaximal, characteristic, complemented
2C2×#11718668C211yesmaximal, characteristic
3#13120041C211yesmaximal, characteristic, complemented
4#13116171C212yesmaximal, complemented
5#13116161C212yesmaximal, complemented
6#13115794C211yesmaximal, characteristic, complemented
7#13115777C211yesmaximal, characteristic, complemented
8#13115097C212yesmaximal
9#13115083C212yesmaximal
10#13114661C211yesmaximal, characteristic
11C2×C13×#554C211yesmaximal, characteristic
12C13×#554—24no—
13C13×#554—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#125C2211yescharacteristic
16C2×C13×#125C2211yescharacteristic
17C2×C13×C22⋊Q8—21no—
18C2×C13×C22⋊Q8—21no—
19C2×C13×C22⋊Q8—21no—
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×D4×C13C2211yescharacteristic
22C2×C4×D4×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C22×C13×C4⋊C4—21no—
25C2×#88123C2211yescharacteristic
26#11718891—21no—
27C2×#88072C2212yes—
28C2×#88072C2212yes—
29#11718726—24no—
30#11718668—24no—
31#11718640—21no—
32#11718640—21no—
33#11718637—21no—
34C2×#88048C2212yes—
35C2×#88047C2212yes—
36C2×#88047C2212yes—
37C4×C4⋊Dic13C2211yescharacteristic
38#11718589C2212yes—
39#11718589C2212yes—
40C2×C4⋊#1055C2211yescharacteristic
41C2×#88043C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718116C2212yes—
46#11718116C2212yes—
47C22×Q8×C13—21no—
48C22×Q8×C13D411yescharacteristic
49C22×D4×C13C2311yescharacteristic
50C23×C4×C13—21no—
51C23×C4×C13—21no—
52C23×C4×C13—21no—
53C22×Dic26—21no—
54C13×C4⋊Q8—22no—
55C13×C4⋊Q8—22no—
56C13×#125—22no—
57C13×#125—22no—
58C13×#125—22no—
59C13×#125D414yes—
60C13×C22⋊Q8—28no—
61C13×C22⋊Q8—28no—
62C13×C22⋊Q8—28no—
63C4×Q8×C13—22no—
64C4×Q8×C13—22no—
65C4×D4×C13—22no—
66C4×D4×C13—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13D414yes—
71C2×C13×C4⋊C4—28no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4D411yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13C2312yes—
91C2×C4⋊Dic13C2312yes—
92C2×#6101—22no—
93C2×#6101—22no—
94C2×C4×Dic13—21no—
95C22×#1055C2312yes—
96C22×#1055C2312yes—
97#88123—22no—
98#88123—22no—
99#88072—24no—
100#88072Q818yescomplemented
101#88071—22no—
102#88071—22no—
103#88071—21no—
104#88048—24no—
105#88047—24no—
106#88047—24no—
107C4⋊#1055—22no—
108#88043—22no—
109#25850—131nomaximal, Sylow
110C24×C13—21no—
111C2×Q8×C13—24no—
112C2×Q8×C13—22no—
113C2×Q8×C13—22no—
114C2×Q8×C13—41no—
115C2×Q8×C13—82no—
116C2×D4×C13—21no—
117C2×D4×C13—22no—
118C2×D4×C13C2×D412yes—
119C2×D4×C13C2×Q814yes—
120C22×C4×C13—24no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—24no—
125C22×C4×C13—24no—
126C22×C4×C13—42no—
127C22×C4×C13—42no—
128C22×C4×C13—82no—
129C22×C4×C13—82no—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2411yescharacteristic
137C22×Dic13—22no—
138C22×Dic13—22no—
139C2×Dic26—42no—
140C2×Dic26—82no—
141C13×C4⋊C4—24no—
142C13×C4⋊C4—24no—
143C13×C4⋊C4—24no—
144C13×C4⋊C4—22no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—24no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4C2×D412yes—
153C13×C4⋊C4C2×D412yes—
154C13×C4⋊C4C2×D412yes—
155C13×C22⋊C4—24no—
156C13×C22⋊C4—24no—
157C13×C22⋊C4—24no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13C2×D412yes—
163C42×C13C2×D412yes—
164C4⋊Dic13—22no—
165C4⋊Dic13—22no—
166C4⋊Dic13—22no—
167C4⋊Dic13—42no—
168C4⋊Dic13C2×Q814yes—
169#6101—82no—
170#6101—82no—
171C4×Dic13—42no—
172C2×#1055—22no—
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#1055—24no—
176C2×#1055C2×Q814yes—
177C2×#554D1311yescharacteristic
178C2×#501—131no—
179C2×#474—131no—
180#2567—131no—
181#2059—132no—
182#2057—132no—
183#1989—131no—
184#1985—131no—
185#1864—132no—
186#1862—132no—
187#1762—131no—
188C23×C13—22no—
189C23×C13—24no—
190C23×C13—41no—
191C23×C13—41no—
192C23×C13—42no—
193C23×C13C22×D411yescharacteristic
194Q8×C13—44no—
195Q8×C13—84no—
196D4×C13—22no—
197D4×C13—24no—
198D4×C13C4⋊Q814yes—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—22no—
204C2×C4×C13—21no—
205C2×C4×C13—21no—
206C2×C4×C13—21no—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—48no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—84no—
220C2×C4×C13—84no—
221C2×C4×C13#12012yes—
222C2×C4×C13#12012yes—
223C2×C4×C13#13712yes—
224C2×C4×C13C22×D411yescharacteristic
225C2×C4×C13C22×D411yescharacteristic
226C2×C4×C13C22×Q812yes—
227C2×C4×C132−1+412yes—
228C2×Dic13—24no—
229C2×Dic13—42no—
230C2×Dic13—42no—
231C2×Dic13—42no—
232C2×Dic13—42no—
233C2×Dic13—42no—
234Dic26—84no—
235#1055—24no—
236#1055—42no—
237#554—24no—
238#554—24no—
239C2×C4⋊Q8—131no—
240C2×C4⋊Q8C2×D1311yescharacteristic
241C2×#125C2×D1311yescharacteristic
242C2×#125C2×D1311yescharacteristic
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—21no—
246C2×C4×Q8C2×D1311yescharacteristic
247C2×C4×D4C2×D1311yescharacteristic
248C2×C4×D4C2×D1311yescharacteristic
249C2×C4×D4C2×D1311yescharacteristic
250C22×C4⋊C4—21no—
251#501—264no—
252#474—264no—
253C2×#107—132no—
254C2×#107—132no—
255C2×#106—132no—
256C2×C4⋊C8—131no—
257C2×#102—132no—
258C2×#102—132no—
259C2×#97—131no—
260#395—261no—
261#395—261no—
262#391—261no—
263#389—132no—
264#389—132no—
265#384—261no—
266C4×C4⋊C4—131no—
267#340—132no—
268#340—132no—
269#340—132no—
270#336—132no—
271#336—132no—
272C22×C13—24no—
273C22×C13—44no—
274C22×C13—44no—
275C22×C13—42no—
276C22×C13—42no—
277C22×C13C2×#12011yescharacteristic
278C22×C13D4×Q812yes—
279C22×C13C2×#13711yescharacteristic
280C22×C13#57511yescharacteristic
281C22×C13#57612yes—
282C4×C13—22no—
283C4×C13—22no—
284C4×C13—22no—
285C4×C13—41no—
286C4×C13—42no—
287C4×C13—41no—
288C4×C13—41no—
289C4×C13—42no—
290C4×C13—42no—
291C4×C13C2×C4⋊Q811yescharacteristic
292C4×C13#53611yescharacteristic
293C4×C13D4×Q812yes—
294Dic13—44no—
295Dic13—82no—
296C22×Q8—21no—
297C22×Q8—261no—
298C22×Q8C22⋊D1311yescharacteristic
299C22×D4C22×D1311yescharacteristic
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—21no—
303C22×C8—132no—
304C22×C8—132no—
305C4⋊Q8—22no—
306C4⋊Q8—22no—
307C4⋊Q8—262no—
308C4⋊Q8—262no—
309#125—22no—
310#125—22no—
311#125—22no—
312#125C22⋊D1314yes—
313C22⋊Q8—28no—
314C22⋊Q8—28no—
315C22⋊Q8—28no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×D4—22no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4C22⋊D1314yes—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—132no—
331C2×C4⋊C4—132no—
332C2×C4⋊C4—261no—
333C2×C4⋊C4—262no—
334C2×C4⋊C4—262no—
335C2×C4⋊C4C22⋊D1311yescharacteristic
336C2×C4⋊C4C22⋊D1311yescharacteristic
337C2×C4⋊C4C22⋊D1311yescharacteristic
338C2×C4⋊C4C22×D1311yescharacteristic
339C2×C4⋊C4C22×D1311yescharacteristic
340C2×C4⋊C4C22×D1311yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C42—261no—
345C2×C42C22×D1311yescharacteristic
346C2×C42C22×D1311yescharacteristic
347C2×C42C22×D1311yescharacteristic
348#107—264no—
349#107—264no—
350#106—264no—
351C4⋊C8—262no—
352#102—138no—
353#102—264no—
354#97—262no—
355#95—261no—
356#95—262no—
357#95—262no—
358C2×C13—44no—
359C2×C13#243411yescharacteristic
360C2×C13#300711yescharacteristic
361C2×C13#300811yescharacteristic
362C2×C13#338512yes—
363C2×C13#338912yes—
364C24—21no—
365C2×Q8—24no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—41no—
369C2×Q8—82no—
370C2×Q8—522no—
371C2×Q8—1042no—
372C2×D4—22no—
373C2×D4—21no—
374C2×D4Q8×D1314yes—
375C2×D4C2×C22⋊D1312yes—
376C22×C4—24no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—82no—
385C22×C4—82no—
386C22×C4—262no—
387C22×C4—262no—
388C22×C4C2×C22⋊D1311yescharacteristic
389C22×C4C2×C22⋊D1311yescharacteristic
390C22×C4C2×C22⋊D1311yescharacteristic
391C22×C4C2×C22⋊D1311yescharacteristic
392C22×C4C2×C22⋊D1311yescharacteristic
393C22×C4C2×C22⋊D1311yescharacteristic
394C22×C4C23×D1311yescharacteristic
395C2×C8—134no—
396C2×C8—262no—
397C2×C8—262no—
398C2×C8—264no—
399C2×C8—262no—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—134no—
412C4⋊C4—262no—
413C4⋊C4—262no—
414C4⋊C4—262no—
415C4⋊C4—522no—
416C4⋊C4—1042no—
417C4⋊C4—1042no—
418C4⋊C4C2×C22⋊D1312yes—
419C4⋊C4C2×C22⋊D1312yes—
420C4⋊C4C2×C22⋊D1312yes—
421C22⋊C4—24no—
422C22⋊C4—24no—
423C22⋊C4—24no—
424C42—21no—
425C42—21no—
426C42—21no—
427C42—21no—
428C42—522no—
429C42C2×C22⋊D1312yes—
430C42C2×C22⋊D1312yes—
431C13#2585011yescharacteristic, complemented, Sylow
432C23—24no—
433C23—22no—
434C23—41no—
435C23—41no—
436C23—42no—
437C23C22×C22⋊D1311yescharacteristic
438Q8—44no—
439Q8—84no—
440Q8—1044no—
441D4—24no—
442D4—22no—
443D4#8819814yes—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—48no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—84no—
465C2×C4—84no—
466C2×C4—264no—
467C2×C4—522no—
468C2×C4—522no—
469C2×C4—522no—
470C2×C4—522no—
471C2×C4—522no—
472C2×C4#8820512yes—
473C2×C4#8820712yes—
474C2×C4#8820712yes—
475C2×C4C2×Q8×D1312yes—
476C2×C4#8825412yes—
477C2×C4C22×C22⋊D1311yescharacteristic
478C2×C4C22×C22⋊D1311yescharacteristic
479C8—264no—
480C8—522no—
481C22—24no—
482C22—42no—
483C22—42no—
484C22—44no—
485C22—44no—
486C22Q8×C22⋊D1312yes—
487C22#1171952711yescharacteristic
488C22C2×#8820511yescharacteristic
489C22#1171954012yes—
490C22C2×#8820711yescharacteristic
491C4—22no—
492C4—22no—
493C4—22no—
494C4—41no—
495C4—42no—
496C4—41no—
497C4—41no—
498C4—42no—
499C4—42no—
500C4—524no—
501C4—1042no—
502C4C2×#8819811yescharacteristic
503C4Q8×C22⋊D1312yes—
504C4#1171952111yescharacteristic
505C2—44no—
506C2#1311847611yescharacteristic
507C2#1312409611yescharacteristic
508C2#1312410411yescharacteristic
509C2#1312774612yes—
510C2#1312779012yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#554C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenterC2×#554D13
hypocenterC13#25850
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#11718726C2semidirect
3. #13120041C2semidirect
4. #13116171C2semidirect
5. #13116161C2semidirect
6. #13115794C2semidirect
7. #13115777C2semidirect
100. #88072Q8semidirect
431. C13#25850semidirect

Maximal subgroups

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

subgroupindex
C2×#117187262
C2×#117186682
#131200412
#131161712
#131161612
#131157942
#131157772
#131150972
#131150832
#131146612
C2×C13×#5542
#2585013