Finite Group Databasebeta

← #15759482

Subgroups — #15759482

Order 3328.

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

normal subgroups only

This group has 522 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
1#13125608C211yesmaximal, characteristic
2#13117916C211yesmaximal, characteristic
3#13115822C211yesmaximal, characteristic
4#13113409C211yesmaximal, characteristic
5#13112715C211yesmaximal, characteristic
6#13112683C211yesmaximal, characteristic
7C2×C13×#328C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×#88178C2211yescharacteristic
10C2×C13×C22⋊C8C2211yescharacteristic
11C2×C13×#95C2211yescharacteristic
12#11718889C412yescomplemented
13#11718873C2211yescharacteristic
14#11718871—21no—
15C4×C22⋊Dic13—21no—
16C4×C22⋊Dic13C2211yescharacteristic
17C2×C22⋊#1055C2211yescharacteristic
18#11718712—22no—
19#11718711—21no—
20#11718705—21no—
21#11718631C412yescomplemented
22#11718314—21no—
23#11718313—21no—
24#11718310—21no—
25#11718307—21no—
26C13×#328—21no—
27C13×#328—21no—
28#11718118—21no—
29#11718118—21no—
30#11718059—22no—
31C22×Q8×C13C2×C411yescharacteristic
32C23×C4×C13—21no—
33C23×C4×C13C2311yescharacteristic
34C22×Dic26D411yescharacteristic
35C22×C8×C13—21no—
36C13×C22⋊Q8—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C22⋊Dic13—21no—
44C2×C22⋊Dic13—21no—
45C2×C22⋊Dic13D411yescharacteristic
46C2×C22⋊Dic13D411yescharacteristic
47C2×#6107—22no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13D411yescharacteristic
50#88178—21no—
51#88178—21no—
52#88178C2×C412yes—
53#88178D412yes—
54C2×#6101—21no—
55C2×#6101—21no—
56C2×#6101—21no—
57C2×C4×Dic13—21no—
58C2×C4×Dic13—21no—
59C2×C4×Dic13—21no—
60C22×#1055—21no—
61C13×C22⋊C8—21no—
62C13×C22⋊C8—21no—
63C13×#95—21no—
64C13×#95D411yescharacteristic
65C13×#95D411yescharacteristic
66#88075—22no—
67#88071—21no—
68#88071—21no—
69#88071—21no—
70#88071—21no—
71#88071—21no—
72#88071—21no—
73C22⋊#1055—21no—
74C22⋊#1055C2×C412yes—
75#88050—22no—
76#88047—22no—
77#9276—131nomaximal, Sylow
78C24×C13C2×D411yescharacteristic
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—81no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—42no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—81no—
90C22×C4×C13—81no—
91C22×C4×C13C22×C411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13#4111yescharacteristic
96C22×C4×C13#4111yescharacteristic
97C22×Dic13—21no—
98C22×Dic13—21no—
99C22×Dic13—21no—
100C22×Dic13—21no—
101C22×Dic13—41no—
102C2×Dic26—21no—
103C2×Dic26—81no—
104C2×Dic26C22⋊C412yes—
105C2×C8×C13—41no—
106C2×C8×C13—81no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C22⋊Dic13—22no—
114C22⋊Dic13—22no—
115C22⋊Dic13—21no—
116C22⋊Dic13—21no—
117C22⋊Dic13—21no—
118C22⋊Dic13—41no—
119C22⋊Dic13—41no—
120C22⋊Dic13Q1612yescomplemented
121#6107—82no—
122C4⋊Dic13—21no—
123C4⋊Dic13—81no—
124C4⋊Dic13C22⋊C412yes—
125#6101—22no—
126#6101—22no—
127#6101—42no—
128#6101—81no—
129C4×Dic13—42no—
130C4×Dic13—81no—
131C4×Dic13—81no—
132C2×#1055—22no—
133C2×#1055—81no—
134#3189—131no—
135#2368—131no—
136#1996—131no—
137#1520—131no—
138C2×#328D1311yescharacteristic
139#1294—131no—
140#1282—131no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13C4×D411yescharacteristic
144C23×C13#12011yescharacteristic
145C23×C13#12111yescharacteristic
146C23×C13C2×Q1611yescharacteristic
147C23×C13#13511yescharacteristic
148C23×C13#13711yescharacteristic
149C23×C13#13711yescharacteristic
150Q8×C13—42no—
151Q8×C13—81no—
152C2×C4×C13—22no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—82no—
167C2×C4×C13—82no—
168C2×C4×C13—81no—
169C2×C4×C13—81no—
170C2×C4×C13C2×C22⋊C411yescharacteristic
171C2×C4×C13C4×D411yescharacteristic
172C2×C4×C13#12111yescharacteristic
173C2×C4×C13#12311yescharacteristic
174C2×Dic13—22no—
175C2×Dic13—22no—
176C2×Dic13—22no—
177C2×Dic13—41no—
178C2×Dic13—41no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—41no—
182C2×Dic13—41no—
183C2×Dic13—41no—
184C2×Dic13—41no—
185C2×Dic13—41no—
186C2×Dic13—81no—
187C2×Dic13—81no—
188C2×Dic13—81no—
189Dic26—42no—
190Dic26—81no—
191C8×C13—81no—
192#1055—42no—
193C2×C22⋊Q8—131no—
194C2×C22⋊Q8C2×D1311yescharacteristic
195#484—132no—
196#484—261no—
197#467—262no—
198#451—132no—
199#451—261no—
200C2×C22⋊C8—131no—
201C2×C22⋊C8C2×D1311yescharacteristic
202#391—261no—
203#387—261no—
204#387—261no—
205#385—261no—
206#380—131no—
207C4×C4⋊C4—261no—
208C4×C22⋊C4—131no—
209C4×C22⋊C4—261no—
210C2×#95C2×D1311yescharacteristic
211#342—261no—
212#342—261no—
213#328—21no—
214#328—21no—
215#328—262no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—41no—
223C22×C13—41no—
224C22×C13—41no—
225C22×C13—41no—
226C22×C13#38611yescharacteristic
227C22×C13C4×Q1611yescharacteristic
228C22×C13#44111yescharacteristic
229C22×C13#45111yescharacteristic
230C22×C13#45211yescharacteristic
231C22×C13#46211yescharacteristic
232C22×C13#46411yescharacteristic
233C4×C13—21no—
234C4×C13—21no—
235C4×C13—21no—
236C4×C13—21no—
237C4×C13—42no—
238C4×C13—81no—
239C4×C13—81no—
240C4×C13—81no—
241Dic13—42no—
242Dic13—42no—
243Dic13—42no—
244Dic13—81no—
245Dic13—161no—
246C22×Q8—131no—
247C22×Q8C4×D1311yescharacteristic
248C23×C4—21no—
249C23×C4C22×D1311yescharacteristic
250C2×Q16—262no—
251C22×C8—21no—
252C22×C8—261no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—132no—
258C22⋊Q8—132no—
259C22⋊Q8—261no—
260C22⋊Q8—261no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—131no—
263C2×C4⋊C4—261no—
264C2×C4⋊C4—261no—
265C2×C4⋊C4—261no—
266C2×C4⋊C4—261no—
267C2×C4⋊C4C4×D1311yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—131no—
270C2×C22⋊C4—131no—
271C2×C22⋊C4—261no—
272C2×C22⋊C4—261no—
273C2×C42—261no—
274C2×C42—261no—
275C2×C42—261no—
276#107—262no—
277#103—262no—
278#103—262no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—132no—
282C22⋊C8—261no—
283#95—21no—
284#95—261no—
285#95—261no—
286#95—261no—
287#95—261no—
288#95—261no—
289#95—261no—
290#95C22⋊D1311yescharacteristic
291#95C22⋊D1311yescharacteristic
292C2×C13—21no—
293C2×C13—21no—
294C2×C13—21no—
295C2×C13—21no—
296C2×C13—21no—
297C2×C13—21no—
298C2×C13#187811yescharacteristic
299C2×C13#190611yescharacteristic
300C2×C13#191311yescharacteristic
301C24D4×D1311yescharacteristic
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—81no—
305C2×Q8—132no—
306C2×Q8—261no—
307C2×Q8—1041no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—81no—
316C22×C4—81no—
317C22×C4—261no—
318C22×C4—261no—
319C22×C4—261no—
320C22×C4—261no—
321C22×C4—521no—
322C22×C4C2×C4×D1311yescharacteristic
323C22×C4#612711yescharacteristic
324C22×C4D4×D1311yescharacteristic
325C22×C4D4×D1311yescharacteristic
326C22×C4#612911yescharacteristic
327C22×C4C2×C22⋊D1311yescharacteristic
328Q16—1042no—
329C2×C8—41no—
330C2×C8—81no—
331C2×C8—262no—
332C2×C8—1041no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—132no—
338C4⋊C4—261no—
339C4⋊C4—262no—
340C4⋊C4—262no—
341C4⋊C4—522no—
342C4⋊C4—1041no—
343C4⋊C4—1041no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—132no—
347C22⋊C4—262no—
348C22⋊C4—262no—
349C22⋊C4—261no—
350C22⋊C4—261no—
351C22⋊C4—261no—
352C22⋊C4—521no—
353C22⋊C4—521no—
354C42—522no—
355C42—1041no—
356C42—1041no—
357C13#927611yescharacteristic, complemented, Sylow
358C23—41no—
359C23—41no—
360C23#8813511yescharacteristic
361C23#8813811yescharacteristic
362C23#8816911yescharacteristic
363C23#8817011yescharacteristic
364C23Q16×D1311yescharacteristic
365C23#8817211yescharacteristic
366C23#8819111yescharacteristic
367Q8—42no—
368Q8—81no—
369Q8—522no—
370Q8—1041no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—262no—
390C2×C4—262no—
391C2×C4—262no—
392C2×C4—521no—
393C2×C4—521no—
394C2×C4—521no—
395C2×C4—521no—
396C2×C4—521no—
397C2×C4—521no—
398C2×C4—521no—
399C2×C4—521no—
400C2×C4—521no—
401C2×C4—1041no—
402C2×C4—1041no—
403C2×C4—1041no—
404C2×C4C22⋊C4×D1311yescharacteristic
405C2×C4#8813711yescharacteristic
406C2×C4C4×C22⋊D1311yescharacteristic
407C2×C4#8819211yescharacteristic
408C8—81no—
409C8—522no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22#1171845011yescharacteristic
421C22#1171845111yescharacteristic
422C22#1171845411yescharacteristic
423C22#1171845911yescharacteristic
424C22#1171861711yescharacteristic
425C22#1171883411yescharacteristic
426C22#1171884711yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—81no—
433C4—81no—
434C4—81no—
435C4—522no—
436C4—522no—
437C4—522no—
438C4—1041no—
439C4—2081no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—21no—
444C2—21no—
445C2—21no—
446C2#1311517411yescharacteristic
447C2#1311534011yescharacteristic
448C2#1311537511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#328C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#328D13
hypocenterC13#9276
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
12. #11718889C4semidirect
21. #11718631C4semidirect
120. C22⋊Dic13Q16semidirect
357. C13#9276semidirect

Maximal subgroups

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

subgroupindex
#131256082
#131179162
#131158222
#131134092
#131127152
#131126832
C2×C13×#3282
#927613