Finite Group Databasebeta

← #15781225

Subgroups — #15781225

Order 3328.

628 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718131C212yesmaximal, complemented
2C2×#11718128C212yesmaximal
3#13114828C211yesmaximal, characteristic, complemented
4C4×#88074C211yesmaximal, characteristic, complemented
5C13×#2534C211yesmaximal, characteristic
6C2×C13×#123C2211yescharacteristic
7C2×C13×#120C2211yescharacteristic
8C2×C4×D4×C13C2211yescharacteristic
9C22×C13×C22⋊C4C411yescharacteristic, complemented
10C13×#396—21no—
11C13×#394—21no—
12C13×#388—21no—
13C13×#386—21no—
14C13×#381C411yescharacteristic, complemented
15C13×#380C411yescharacteristic, complemented
16C13×#379C411yescharacteristic, complemented
17C2×#88074C2212yes—
18C2×#88073C2212yes—
19C4×C22⋊Dic13—21no—
20#11718585—21no—
21#11718131—24no—
22#11718128—24no—
23#11718122—21no—
24#11718118—21no—
25C25×C13C2×C411yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13C2311yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13C2×C411yescharacteristic
30C23×C4×C13D411yescharacteristic
31C13×#123—22no—
32C13×#123—22no—
33C13×#120—22no—
34C13×#120—22no—
35C4×D4×C13—41no—
36C4×D4×C13—41no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—41no—
47C2×C13×C22⋊C4—41no—
48C2×C13×C22⋊C4C2×C411yescharacteristic
49C2×C13×C22⋊C4C2×C411yescharacteristic
50C2×C13×C22⋊C4C2×C411yescharacteristic
51C2×C13×C22⋊C4D411yescharacteristic
52C2×C42×C13D411yescharacteristic
53C2×C22⋊Dic13—22no—
54C2×C4×Dic13—41no—
55C2×#6099—22no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59#88074—22no—
60#88074D414yes—
61#88073—22no—
62#88073—22no—
63#88071—41no—
64C4⋊#1055—41no—
65C4⋊#1055—41no—
66#13222—131nomaximal, Sylow
67C24×C13—21no—
68C24×C13—22no—
69C24×C13—41no—
70C24×C13—42no—
71C24×C13—41no—
72C24×C13—81no—
73C24×C13C22×C411yescharacteristic
74C24×C13C2×D411yescharacteristic
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—42no—
78C2×D4×C13—42no—
79C2×D4×C13—81no—
80C2×D4×C13C2×D412yes—
81C2×D4×C13#4112yes—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—22no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—81no—
93C22×C4×C13—81no—
94C22×C4×C13C22⋊C411yescharacteristic
95C22×C4×C13C22⋊C411yescharacteristic
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22⋊C411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×Dic13—42no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—81no—
104C13×C22⋊C4—22no—
105C13×C22⋊C4—22no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—42no—
109C13×C22⋊C4—42no—
110C13×C22⋊C4—42no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—41no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—81no—
116C42×C13—21no—
117C42×C13—21no—
118C22⋊Dic13—24no—
119C22⋊Dic13—42no—
120C4×Dic13—82no—
121#6099—42no—
122#6099—42no—
123C2×#1055—42no—
124#2534D1311yescharacteristic
125C2×#352—132no—
126C2×AΣL(1,𝔽16)—132no—
127#1800—131no—
128C4×#99—131no—
129C23×C13—21no—
130C23×C13—21no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—22no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—42no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13—42no—
146C23×C13—82no—
147C23×C13—84no—
148C23×C13—84no—
149C23×C13—82no—
150C23×C13C2×C22⋊C411yescharacteristic
151C23×C13C4×D412yes—
152C23×C13#12112yes—
153D4×C13—42no—
154D4×C13—42no—
155D4×C13—84no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—41no—
162C2×C4×C13—42no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—81no—
176C2×C4×C13—81no—
177C2×C4×C13—81no—
178C2×C4×C13—82no—
179C2×C4×C13#9911yescharacteristic
180C2×C4×C13#9911yescharacteristic
181C2×C4×C13#12411yescharacteristic
182C2×C4×C13#12711yescharacteristic
183C2×Dic13—44no—
184C2×Dic13—82no—
185C2×Dic13—82no—
186#1055—82no—
187C2×#123C2×D1311yescharacteristic
188C2×#120C2×D1311yescharacteristic
189C2×C4×D4C2×D1311yescharacteristic
190C22×C22⋊C4Dic1311yescharacteristic, complemented
191#423—261no—
192C2×#100—132no—
193C2×#99—132no—
194#396—21no—
195#394—21no—
196#388—21no—
197#386—21no—
198#381Dic1311yescharacteristic, complemented
199#380Dic1311yescharacteristic, complemented
200#379Dic1311yescharacteristic, complemented
201C4×C22⋊C4—261no—
202#352—264no—
203AΣL(1,𝔽16)—264no—
204#343—261no—
205#342—261no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—22no—
209C22×C13—22no—
210C22×C13—42no—
211C22×C13—42no—
212C22×C13—42no—
213C22×C13—42no—
214C22×C13—42no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—41no—
218C22×C13—41no—
219C22×C13—42no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13—81no—
223C22×C13—84no—
224C22×C13—84no—
225C22×C13—81no—
226C22×C13—81no—
227C22×C13#39011yescharacteristic
228C22×C13C2×#9911yescharacteristic
229C22×C13#41011yescharacteristic
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—21no—
233C4×C13—21no—
234C4×C13—41no—
235C4×C13—41no—
236C4×C13—41no—
237C4×C13—81no—
238C4×C13—81no—
239C4×C13—81no—
240Dic13—84no—
241C25C2×Dic1311yescharacteristic
242C22×D4—21no—
243C22×D4C22×D1311yescharacteristic
244C23×C4C2×Dic1311yescharacteristic
245C23×C4C2×Dic1311yescharacteristic
246C23×C4C22⋊D1311yescharacteristic
247C2×M16—262no—
248#123—22no—
249#123—22no—
250#120—22no—
251#120—22no—
252C4×D4—41no—
253C4×D4—41no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4C22⋊D1311yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—41no—
264C2×C22⋊C4—41no—
265C2×C22⋊C4—262no—
266C2×C22⋊C4C2×Dic1311yescharacteristic
267C2×C22⋊C4C2×Dic1311yescharacteristic
268C2×C22⋊C4C2×Dic1311yescharacteristic
269C2×C22⋊C4C22⋊D1311yescharacteristic
270C2×C42—521no—
271C2×C42C22⋊D1311yescharacteristic
272C4⋊C8—521no—
273C4⋊C8—521no—
274#100—262no—
275#100—262no—
276#99—134no—
277#99—262no—
278#95—21no—
279#95—21no—
280#95—21no—
281#95—521no—
282C2×C13—21no—
283C2×C13—21no—
284C2×C13—42no—
285C2×C13—42no—
286C2×C13—82no—
287C2×C13#196411yescharacteristic
288C2×C13#212011yescharacteristic
289C2×C13#212111yescharacteristic
290C24—21no—
291C24—22no—
292C24—41no—
293C24—42no—
294C24—41no—
295C24—81no—
296C24C22×Dic1311yescharacteristic
297C24C2×C22⋊D1311yescharacteristic
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—42no—
301C2×D4—42no—
302C2×D4—81no—
303C2×D4D4×D1312yes—
304C2×D4#612912yes—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—81no—
316C22×C4—81no—
317C22×C4—522no—
318C22×C4C22⋊Dic1311yescharacteristic
319C22×C4C22⋊Dic1311yescharacteristic
320C22×C4C22⋊Dic1311yescharacteristic
321C22×C4C22⋊Dic1311yescharacteristic
322C22×C4C2×C22⋊D1311yescharacteristic
323M16—522no—
324M16—522no—
325C2×C8—522no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—81no—
330C22⋊C4—22no—
331C22⋊C4—22no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—81no—
342C22⋊C4—264no—
343C22⋊C4—522no—
344C42—21no—
345C42—21no—
346C42—1042no—
347C13#1322211yescharacteristic, complemented, Sylow
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—22no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—42no—
361C23—42no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—82no—
366C23—84no—
367C23—84no—
368C23—82no—
369C23D4×Dic1312yes—
370C23#8819212yes—
371C23C2×C22⋊Dic1311yescharacteristic
372D4—42no—
373D4—42no—
374D4—84no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—82no—
398C2×C4—524no—
399C2×C4—1042no—
400C2×C4—1042no—
401C2×C4#8807411yescharacteristic
402C2×C4#8807411yescharacteristic
403C2×C4#8819011yescharacteristic
404C2×C4#8819411yescharacteristic
405C8—1042no—
406C22—21no—
407C22—21no—
408C22—22no—
409C22—22no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—42no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—84no—
424C22—84no—
425C22—81no—
426C22—81no—
427C22C2×#8807411yescharacteristic
428C22#1171888211yescharacteristic
429C22#1171890111yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4—1044no—
441C2—21no—
442C2—21no—
443C2—42no—
444C2—42no—
445C2—82no—
446C2#1311567311yescharacteristic
447C2#1311647711yescharacteristic
448C2#1311648211yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2534C2
socleC22×C13C2×#99
prime radicalC2×C13×#120C22
cosocleC22×D4×C13C23
hypercenter#2534D13
hypocenterC13#13222
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2534

Complements

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

NH ≅ G/Ntype
1. C2×#11718131C2semidirect
3. #13114828C2semidirect
4. C4×#88074C2semidirect
9. C22×C13×C22⋊C4C4semidirect
14. C13×#381C4semidirect
15. C13×#380C4semidirect
16. C13×#379C4semidirect
190. C22×C22⋊C4Dic13semidirect
198. #381Dic13semidirect
199. #380Dic13semidirect
200. #379Dic13semidirect
347. C13#13222semidirect

Maximal subgroups

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

subgroupindex
C2×#117181312
C2×#117181282
#131148282
C4×#880742
C13×#25342
#1322213