Finite Group Databasebeta

← #15757999

Subgroups — #15757999

Order 3328.

670 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 111 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
1#13123865C211yesmaximal, characteristic, complemented
2C4×#88073C211yesmaximal, characteristic, complemented
3#13113279C212yesmaximal, complemented
4#13112729C212yesmaximal, complemented
5C13×#2397C211yesmaximal, characteristic
6C2×C4×D4×C13—21no—
7C2×C4×D4×C13—21no—
8C2×C4×D4×C13C2211yescharacteristic
9C2×C4×D4×C13C2211yescharacteristic
10C13×#399—21no—
11C13×#399C411yescharacteristic
12C13×#399C411yescharacteristic
13C13×#392—21no—
14C13×#392C411yescharacteristic
15C13×#392C411yescharacteristic
16C13×#376C2211yescharacteristic
17C2×#88073—21no—
18#11718868—21no—
19C2×C22⋊#1055—21no—
20#11718672—24no—
21#11718587C2212yes—
22C4×#6099C2212yes—
23D4⋊#1055—24no—
24#11718122—21no—
25C22×D4×C13—21no—
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic
28C22×D4×C13D411yescharacteristic
29C23×C4×C13—21no—
30C23×C4×C13D411yescharacteristic
31C23×C4×C13D411yescharacteristic
32C4×D4×C13—22no—
33C4×D4×C13—22no—
34C4×D4×C13—22no—
35C4×D4×C13—22no—
36C4×D4×C13—44no—
37C4×D4×C13—44no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4C2×C411yescharacteristic
41C2×C13×C4⋊C4D411yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4C2×C411yescharacteristic
48C2×C13×C22⋊C4C2×C411yescharacteristic
49C2×C42×C13—21no—
50C2×C42×C13C2311yescharacteristic
51C2×#6099—22no—
52C2×#6099—22no—
53C22×#1055—22no—
54C13×#95—21no—
55C13×#95C2×C411yescharacteristic
56C13×#95C2×C411yescharacteristic
57#88073—24no—
58C22⋊#1055—22no—
59C22⋊#1055—22no—
60C22⋊#1055—22no—
61C4⋊#1055D414yescomplemented
62#88043—22no—
63#88043—22no—
64C4×#1055—22no—
65#9031—131nomaximal, Sylow
66C24×C13—21no—
67C24×C13C22⋊C411yescharacteristic
68C24×C13C22⋊C411yescharacteristic
69C2×D4×C13—22no—
70C2×D4×C13—22no—
71C2×D4×C13—22no—
72C2×D4×C13—41no—
73C2×D4×C13—42no—
74C2×D4×C13—42no—
75C2×D4×C13—42no—
76C2×D4×C13—42no—
77C2×D4×C13—42no—
78C2×D4×C13—42no—
79C2×D4×C13—42no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—42no—
88C22×C4×C13—42no—
89C22×C4×C13—42no—
90C22×C4×C13—42no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13C22⋊C411yescharacteristic
94C22×C4×C13C22⋊C411yescharacteristic
95C22×C4×C13C22×C411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—42no—
101C13×C4⋊C4—42no—
102C13×C22⋊C4—22no—
103C13×C22⋊C4—22no—
104C13×C22⋊C4—42no—
105C13×C22⋊C4—42no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—42no—
108C13×C22⋊C4—42no—
109C42×C13—24no—
110C42×C13C2×D412yes—
111C42×C13#4112yes—
112#6099—24no—
113#6099—42no—
114#6099—82no—
115C2×#1055—24no—
116C2×#1055—42no—
117C2×#1055—82no—
118#2973—131no—
119#2397D1311yescharacteristic
120C4×#100—131no—
121#1490—132no—
122#1300—132no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—22no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13#10412yes—
140C23×C13C2×C22⋊C411yescharacteristic
141D4×C13—24no—
142D4×C13—44no—
143D4×C13—42no—
144D4×C13—48no—
145D4×C13—48no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—22no—
149C2×C4×C13—22no—
150C2×C4×C13—22no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C2×C4×C13—82no—
168C2×C4×C13—82no—
169C2×C4×C13C4×D412yes—
170C2×C4×C13#12011yescharacteristic
171C2×C4×C13#12112yes—
172C2×C4×C13#12311yescharacteristic
173#1055—44no—
174#1055—44no—
175C2×C4×D4—21no—
176C2×C4×D4—21no—
177C2×C4×D4C2×D1311yescharacteristic
178C2×C4×D4C2×D1311yescharacteristic
179#435—264no—
180#432—132no—
181C2×#100—261no—
182#407—261no—
183C2×C22⋊C8—261no—
184C4×M16—132no—
185#399—21no—
186#399Dic1311yescharacteristic
187#399Dic1311yescharacteristic
188#392—21no—
189#392Dic1311yescharacteristic
190#392Dic1311yescharacteristic
191#376C2×D1311yescharacteristic
192#343—261no—
193D4⋊C8—264no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—22no—
197C22×C13—42no—
198C22×C13—42no—
199C22×C13—42no—
200C22×C13—42no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—42no—
206C22×C13—41no—
207C22×C13—81no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13#38611yescharacteristic
214C22×C13C2×#10411yescharacteristic
215C22×C13#42111yescharacteristic
216C4×C13—22no—
217C4×C13—21no—
218C4×C13—22no—
219C4×C13—42no—
220C4×C13—42no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—81no—
224C4×C13#45312yes—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4C2×Dic1311yescharacteristic
228C22×D4C22⋊D1311yescharacteristic
229C23×C4—21no—
230C23×C4C22⋊D1311yescharacteristic
231C23×C4C22⋊D1311yescharacteristic
232C2×M16—262no—
233C2×M16—262no—
234C22×C8—262no—
235C4×D4—22no—
236C4×D4—22no—
237C4×D4—22no—
238C4×D4—22no—
239C4×D4—44no—
240C4×D4—44no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C2×Dic1311yescharacteristic
244C2×C4⋊C4C22⋊D1311yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4C2×Dic1311yescharacteristic
251C2×C22⋊C4C2×Dic1311yescharacteristic
252C2×C42—21no—
253C2×C42C22×D1311yescharacteristic
254C4⋊C8—134no—
255#100—264no—
256C22⋊C8—262no—
257C22⋊C8—262no—
258C22⋊C8—262no—
259#97—262no—
260#97—262no—
261C4×C8—262no—
262#95—21no—
263#95C2×Dic1311yescharacteristic
264#95C2×Dic1311yescharacteristic
265C2×C13—21no—
266C2×C13—21no—
267C2×C13—42no—
268C2×C13—81no—
269C2×C13—82no—
270C2×C13#187111yescharacteristic
271C2×C13#188711yescharacteristic
272C2×C13#189111yescharacteristic
273C24—21no—
274C24C22⋊Dic1311yescharacteristic
275C24C22⋊Dic1311yescharacteristic
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—41no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4C22⋊Dic1311yescharacteristic
301C22×C4C22⋊Dic1311yescharacteristic
302C22×C4C22×Dic1311yescharacteristic
303C22×C4C2×C22⋊D1311yescharacteristic
304C22×C4C2×C22⋊D1311yescharacteristic
305M16—264no—
306M16—522no—
307M16—1042no—
308C2×C8—264no—
309C2×C8—522no—
310C2×C8—1042no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C42—24no—
323C42D4×D1312yes—
324C42#612912yes—
325C13#903111yescharacteristic, complemented, Sylow
326C23—21no—
327C23—21no—
328C23—22no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23#8807712yes—
343C23C2×C22⋊Dic1311yescharacteristic
344D4—24no—
345D4—44no—
346D4—42no—
347D4—48no—
348D4—48no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4D4×Dic1312yes—
373C2×C4#8818911yescharacteristic
374C2×C4#8819111yescharacteristic
375C2×C4#8819312yes—
376C8—524no—
377C8—524no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—42no—
390C22—41no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22#1171888111yescharacteristic
398C22C2×#8807711yescharacteristic
399C22#1171889711yescharacteristic
400C4—22no—
401C4—21no—
402C4—22no—
403C4—42no—
404C4—42no—
405C4—41no—
406C4—41no—
407C4—81no—
408C4#1171873812yes—
409C2—21no—
410C2—21no—
411C2—42no—
412C2—81no—
413C2—82no—
414C2#1311513911yescharacteristic
415C2#1311523511yescharacteristic
416C2#1311525511yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#2397C2
socleC22×C13#386
cosocleC2×C42×C13C23
hypercenter#2397D13
hypocenterC13#9031
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. #13123865C2semidirect
2. C4×#88073C2semidirect
3. #13113279C2semidirect
4. #13112729C2semidirect
61. C4⋊#1055D4semidirect
325. C13#9031semidirect

Maximal subgroups

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

subgroupindex
#131238652
C4×#880732
#131132792
#131127292
C13×#23972
#903113