Finite Group Databasebeta

← #15763221

Subgroups — #15763221

Order 3328.

610 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 113 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×#11718631C211yesmaximal, characteristic
2#13120652C211yesmaximal, characteristic
3C2×#11718643C211yesmaximal, characteristic
4C2×#11718059C211yesmaximal, characteristic
5C2×#11718061C211yesmaximal, characteristic
6#13112714C211yesmaximal, characteristic
7C13×#1824C211yesmaximal, characteristic
8C22×C13×C4⋊C4C2211yescharacteristic
9C2×#88178C2211yescharacteristic
10C22×#6101C2211yescharacteristic
11C2×C13×C22⋊C8C2211yescharacteristic
12C13×#380C2211yescharacteristic
13C2×#88071—21no—
14C2×#88071—21no—
15C2×#88071C2211yescharacteristic
16C2×C22⋊#1055C2211yescharacteristic
17#11718644—22no—
18#11718643—22no—
19#11718643—22no—
20#11718631—22no—
21#11718631—22no—
22C2×#88050—21no—
23C2×#88047—21no—
24#11718611—21no—
25#11718604—21no—
26#11718320—21no—
27#11718317—21no—
28C13×#340—22no—
29#11718061—22no—
30#11718059—22no—
31C23×C4×C13—21no—
32C23×C4×C13C2311yescharacteristic
33C23×Dic13—21no—
34C23×Dic13D411yescharacteristic
35C23×Dic13D411yescharacteristic
36C22×Dic26D411yescharacteristic
37C22×C8×C13—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4D412yes—
44C2×C13×C4⋊C4D412yes—
45C2×C13×C22⋊C4—21no—
46C2×C22⋊Dic13—21no—
47C2×C4⋊Dic13—22no—
48C2×C4⋊Dic13D411yescharacteristic
49#88178—21no—
50#88178—21no—
51#88178—21no—
52#88178—21no—
53C2×#6101—21no—
54C2×#6101—21no—
55C2×#6101—21no—
56C2×#6101—21no—
57C2×#6101—21no—
58C2×#6101—21no—
59C2×#6101—21no—
60C22×#1055—21no—
61C13×C22⋊C8—21no—
62C13×C22⋊C8—21no—
63C13×#95—21no—
64#88071—22no—
65#88071—22no—
66#88071—22no—
67#88071—24no—
68#88071—24no—
69#88071—21no—
70#88071D412yes—
71C22⋊#1055—21no—
72C22⋊#1055D412yes—
73#88050—24no—
74#88047—24no—
75#9929—131nomaximal, Sylow
76C24×C13C2×D411yescharacteristic
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—42no—
80C22×C4×C13—44no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13#4111yescharacteristic
89C22×Dic13—21no—
90C22×Dic13—21no—
91C22×Dic13—21no—
92C22×Dic13—21no—
93C22×Dic13—21no—
94C22×Dic13—21no—
95C22×Dic13—22no—
96C22×Dic13—21no—
97C22×Dic13—21no—
98C22×Dic13—21no—
99C22×Dic13—21no—
100C22×Dic13—21no—
101C22×Dic13—42no—
102C22×Dic13—42no—
103C22×Dic13—42no—
104C22×Dic13—41no—
105C22×Dic13—41no—
106C22×Dic13Q1612yes—
107C2×Dic26—21no—
108C2×Dic26—21no—
109C2×Dic26—42no—
110C2×C8×C13—42no—
111C2×C8×C13—41no—
112C13×C4⋊C4—22no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—42no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—41no—
119C22⋊Dic13—41no—
120C22⋊Dic13—41no—
121C4⋊Dic13—21no—
122C4⋊Dic13—21no—
123C4⋊Dic13—82no—
124#6101—41no—
125#6101—41no—
126#6101—41no—
127#6101—41no—
128#6101—41no—
129#6101—41no—
130C2×#1055—22no—
131C2×#1055—42no—
132C2×#484—131no—
133#2627—131no—
134C2×#400—131no—
135#1824D1311yescharacteristic
136C2×#328—131no—
137C2×#324—131no—
138#1294—131no—
139C23×C13—22no—
140C23×C13—22no—
141C23×C13#12011yescharacteristic
142C23×C13#12011yescharacteristic
143C23×C13#12111yescharacteristic
144C23×C13C2×Q1611yescharacteristic
145C23×C13#13511yescharacteristic
146C23×C13#13711yescharacteristic
147C23×C13#13711yescharacteristic
148C2×C4×C13—22no—
149C2×C4×C13—22no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—44no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—82no—
160C2×C4×C13—82no—
161C2×C4×C13#12011yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12711yescharacteristic
165C2×Dic13—22no—
166C2×Dic13—22no—
167C2×Dic13—22no—
168C2×Dic13—41no—
169C2×Dic13—41no—
170C2×Dic13—41no—
171C2×Dic13—41no—
172C2×Dic13—42no—
173C2×Dic13—42no—
174C2×Dic13—42no—
175C2×Dic13—41no—
176C2×Dic13—41no—
177C2×Dic13—41no—
178C2×Dic13—42no—
179C2×Dic13—42no—
180C2×Dic13—42no—
181C2×Dic13—42no—
182C2×Dic13—82no—
183C2×Dic13—82no—
184C2×Dic13—81no—
185Dic26—42no—
186Dic26—81no—
187C8×C13—81no—
188#1055—42no—
189C2×C22⋊Q8—131no—
190C22×C4⋊C4—131no—
191C22×C4⋊C4C2×D1311yescharacteristic
192#484—262no—
193#484—262no—
194C2×#107—261no—
195C2×#103—261no—
196C2×C22⋊C8—131no—
197C2×C22⋊C8C2×D1311yescharacteristic
198#400—261no—
199#400—262no—
200#400—262no—
201#398—262no—
202#395—261no—
203#385—261no—
204#381—261no—
205#380C2×D1311yescharacteristic
206C2×#95—131no—
207C2×#95—261no—
208C2×#95—261no—
209#340—22no—
210#328—262no—
211#324—262no—
212C22×C13—22no—
213C22×C13—22no—
214C22×C13—22no—
215C22×C13—22no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13#39211yescharacteristic
221C22×C13#45111yescharacteristic
222C22×C13#45111yescharacteristic
223C22×C13#45211yescharacteristic
224C22×C13#45211yescharacteristic
225C22×C13#45412yes—
226C22×C13#45812yes—
227C22×C13#46711yescharacteristic
228C22×C13#47011yescharacteristic
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—21no—
233C4×C13—82no—
234C4×C13—82no—
235Dic13—42no—
236Dic13—82no—
237Dic13—81no—
238Dic13—81no—
239Dic13—81no—
240C22×Q8—131no—
241C23×C4—21no—
242C23×C4—131no—
243C23×C4—131no—
244C23×C4—261no—
245C23×C4C22×D1311yescharacteristic
246C22×C8—21no—
247C22×C8—261no—
248C22⋊Q8—261no—
249C22⋊Q8—261no—
250C22⋊Q8—261no—
251C22⋊Q8—261no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—131no—
258C2×C4⋊C4—261no—
259C2×C4⋊C4—261no—
260C2×C4⋊C4—261no—
261C2×C4⋊C4—261no—
262C2×C4⋊C4—261no—
263C2×C4⋊C4—261no—
264C2×C4⋊C4—261no—
265C2×C4⋊C4—262no—
266C2×C4⋊C4D5212yes—
267C2×C4⋊C4C22⋊D1312yes—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—261no—
270#107—264no—
271#103—264no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274C22⋊C8—132no—
275C22⋊C8—261no—
276#95—21no—
277#95—132no—
278#95—264no—
279#95—264no—
280#95—262no—
281#95—262no—
282#95—262no—
283#95—261no—
284C2×C13—21no—
285C2×C13—21no—
286C2×C13—21no—
287C2×C13—21no—
288C2×C13#161512yes—
289C2×C13#161712yes—
290C2×C13#200111yescharacteristic
291C2×C13#200311yescharacteristic
292C2×C13#202211yescharacteristic
293C24D4×D1311yescharacteristic
294C2×Q8—261no—
295C2×Q8—261no—
296C2×Q8—522no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—42no—
300C22×C4—44no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—132no—
304C22×C4—261no—
305C22×C4—261no—
306C22×C4—261no—
307C22×C4—261no—
308C22×C4—261no—
309C22×C4—261no—
310C22×C4—262no—
311C22×C4—261no—
312C22×C4—261no—
313C22×C4—261no—
314C22×C4—261no—
315C22×C4—261no—
316C22×C4—522no—
317C22×C4—522no—
318C22×C4—522no—
319C22×C4—521no—
320C22×C4—521no—
321C22×C4C2×D5211yescharacteristic
322C22×C4#612711yescharacteristic
323C22×C4D4×D1311yescharacteristic
324C22×C4D4×D1311yescharacteristic
325C22×C4D4×D1311yescharacteristic
326C22×C4C2×C22⋊D1311yescharacteristic
327C2×C8—42no—
328C2×C8—41no—
329C2×C8—262no—
330C2×C8—522no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—42no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—261no—
337C4⋊C4—261no—
338C4⋊C4—521no—
339C4⋊C4—521no—
340C4⋊C4—521no—
341C4⋊C4—521no—
342C4⋊C4—521no—
343C4⋊C4—521no—
344C4⋊C4—1042no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—521no—
348C22⋊C4—521no—
349C13#992911yescharacteristic, complemented, Sylow
350C23—22no—
351C23—22no—
352C23#8813611yescharacteristic
353C23#8813811yescharacteristic
354C23#8816911yescharacteristic
355C23#8817011yescharacteristic
356C23Q16×D1311yescharacteristic
357C23#8817211yescharacteristic
358C23#8819111yescharacteristic
359Q8—522no—
360Q8—1041no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—44no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—262no—
375C2×C4—262no—
376C2×C4—262no—
377C2×C4—521no—
378C2×C4—521no—
379C2×C4—521no—
380C2×C4—521no—
381C2×C4—522no—
382C2×C4—522no—
383C2×C4—522no—
384C2×C4—522no—
385C2×C4—522no—
386C2×C4—522no—
387C2×C4—522no—
388C2×C4—521no—
389C2×C4—521no—
390C2×C4—521no—
391C2×C4—1042no—
392C2×C4—1042no—
393C2×C4—1041no—
394C2×C4#8813611yescharacteristic
395C2×C4#8813811yescharacteristic
396C2×C4#8818411yescharacteristic
397C2×C4#8819411yescharacteristic
398C8—81no—
399C8—522no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22#1171846911yescharacteristic
409C22#1171847111yescharacteristic
410C22#1171847411yescharacteristic
411C22#1171847711yescharacteristic
412C22#1171862111yescharacteristic
413C22#1171871412yes—
414C22#1171883411yescharacteristic
415C22#1171884711yescharacteristic
416C22#1171886212yes—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—82no—
422C4—82no—
423C4—522no—
424C4—1042no—
425C4—1041no—
426C4—1041no—
427C4—1041no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2—21no—
432C2#1311386412yes—
433C2#1311387612yes—
434C2#1311584511yescharacteristic
435C2#1311585911yescharacteristic
436C2#1311596711yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1824C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenter#1824D13
hypocenterC13#9929
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
349. C13#9929semidirect

Maximal subgroups

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

subgroupindex
C2×#117186312
#131206522
C2×#117186432
C2×#117180592
C2×#117180612
#131127142
C13×#18242
#992913