Finite Group Databasebeta

← #34098380

Subgroups — #34098380

Order 20096.

780 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14578933C211yesmaximal, characteristic, complemented
2C22×#14578931C211yesmaximal, characteristic
3C22×#14578931C211yesmaximal, characteristic
4C22×#14578931C211yesmaximal, characteristic
5C2×#19097678C211yesmaximal, characteristic, complemented
6C2×#19097678C211yesmaximal, characteristic, complemented
7C2×#95×C157C211yesmaximal, characteristic, complemented
8C24×D157C2211yescharacteristic
9C23×Dic157C2211yescharacteristic
10C23×Dic157C2211yescharacteristic
11C23×Dic157C2211yescharacteristic
12C2×#14578933—22no—
13C2×#14578933—22no—
14C2×#14578933—22no—
15C2×#14578931—22no—
16C2×#14578931—22no—
17C2×#14578931—22no—
18C2×#14578931—22no—
19C2×#14578931—22no—
20C2×#14578931—22no—
21C2×#14578931—22no—
22C2×#14578931—22no—
23C2×#14578931C414yescomplemented
24#19097678—22no—
25#19097678—22no—
26C23×C4×C157C2211yescharacteristic
27C23×C4×C157C2211yescharacteristic
28C23×C4×C157C2211yescharacteristic
29#95×C157—22no—
30C23×D157—21no—
31C23×D157—21no—
32C23×D157—21no—
33C23×D157—21no—
34C23×D157—21no—
35C23×D157—21no—
36C23×D157—21no—
37C23×D157—21no—
38C23×D157—21no—
39C23×D157—21no—
40C23×D157—21no—
41C23×D157—21no—
42C23×D157C2×C412yes—
43C23×D157D412yes—
44C23×D157Q812yes—
45C22×Dic157—21no—
46C22×Dic157—21no—
47C22×Dic157—21no—
48C22×Dic157—21no—
49C22×Dic157—21no—
50C22×Dic157—21no—
51C22×Dic157—21no—
52C22×Dic157—21no—
53C22×Dic157—21no—
54C22×Dic157—21no—
55C22×Dic157—21no—
56C22×Dic157—21no—
57C22×Dic157—21no—
58C22×Dic157—21no—
59C22×Dic157—21no—
60C22×Dic157—21no—
61C22×Dic157C2×C412yes—
62C22×Dic157D412yes—
63C22×Dic157D412yes—
64C22×Dic157D412yes—
65C22×Dic157D412yes—
66#14578933—28no—
67#14578931—28no—
68#14578931—28no—
69#14578931—28no—
70C24×C157C2311yescharacteristic
71C22×C4×C157—21no—
72C22×C4×C157—21no—
73C22×C4×C157—21no—
74C22×C4×C157—21no—
75C22×C4×C157—21no—
76C22×C4×C157—21no—
77C22×C4×C157—21no—
78C22×C4×C157—21no—
79C22×C4×C157—21no—
80C22×C4×C157—21no—
81C22×C4×C157—21no—
82C22×C4×C157—21no—
83C22×C4×C157—21no—
84C22×C4×C157—21no—
85C22×C4×C157—21no—
86C22×C4×C157—21no—
87C22×C4×C157—21no—
88C22×C4×C157—21no—
89C22×C4×C157C2×C412yes—
90C22×C4×C157D412yes—
91C22×C4×C157D412yes—
92C22×D157—22no—
93C22×D157—22no—
94C22×D157—22no—
95C22×D157—22no—
96C22×D157—22no—
97C22×D157—22no—
98C22×D157—22no—
99C22×D157—22no—
100C22×D157—22no—
101C22×D157—22no—
102C22×D157—22no—
103C22×D157—22no—
104C22×D157—22no—
105C22×D157—22no—
106C22×D157—22no—
107C22×D157—22no—
108C22×D157—22no—
109C22×D157—22no—
110C22×D157—41no—
111C22×D157—41no—
112C22×D157—41no—
113C22×D157—41no—
114C22×D157—41no—
115C22×D157—41no—
116C22×D157—41no—
117C22×D157—41no—
118C22×D157—41no—
119C22×D157—41no—
120C22×D157—41no—
121C22×D157—41no—
122C22×D157—41no—
123C22×D157—41no—
124C22×D157—41no—
125C22×D157—41no—
126C22×D157C4⋊C414yescomplemented
127C2×Dic157—22no—
128C2×Dic157—22no—
129C2×Dic157—22no—
130C2×Dic157—22no—
131C2×Dic157—22no—
132C2×Dic157—22no—
133C2×Dic157—22no—
134C2×Dic157—22no—
135C2×Dic157—22no—
136C2×Dic157—22no—
137C2×Dic157—22no—
138C2×Dic157—22no—
139C2×Dic157—41no—
140C2×Dic157—41no—
141C2×Dic157—41no—
142C2×Dic157—41no—
143C2×Dic157—41no—
144C2×Dic157—41no—
145C2×Dic157—41no—
146C2×Dic157—41no—
147C2×Dic157C22⋊C414yescomplemented
148C23×C157C22×C411yescharacteristic
149C23×C157C2×D411yescharacteristic
150C23×C157C2×D411yescharacteristic
151C23×C157C2×D411yescharacteristic
152C23×C157C2×D411yescharacteristic
153C23×C157C2×D411yescharacteristic
154C23×C157C2×D411yescharacteristic
155C23×C157C2×D411yescharacteristic
156C23×C157C2×Q811yescharacteristic
157C23×C157#4111yescharacteristic
158C23×C157#4111yescharacteristic
159C23×C157#4111yescharacteristic
160C23×C157#4111yescharacteristic
161C23×C157#4111yescharacteristic
162C23×C157#4111yescharacteristic
163C2×C4×C157—22no—
164C2×C4×C157—22no—
165C2×C4×C157—22no—
166C2×C4×C157—22no—
167C2×C4×C157—22no—
168C2×C4×C157—22no—
169C2×C4×C157—22no—
170C2×C4×C157—22no—
171C2×C4×C157—22no—
172C2×C4×C157—41no—
173C2×C4×C157—41no—
174C2×C4×C157—41no—
175C2×C4×C157—41no—
176C2×C4×C157—41no—
177C2×C4×C157—41no—
178C2×C4×C157—41no—
179C2×C4×C157—41no—
180C2×C4×C157—41no—
181C2×C4×C157—41no—
182C2×C4×C157—41no—
183C2×C4×C157—41no—
184C22×C157C2×C22⋊C411yescharacteristic
185C22×C157C2×C4⋊C411yescharacteristic
186C22×C157#11711yescharacteristic
187C22×C157C4×D411yescharacteristic
188C22×C157C4×D411yescharacteristic
189C22×C157C4×D411yescharacteristic
190C22×C157C4×D411yescharacteristic
191C22×C157#12011yescharacteristic
192C22×C157#12011yescharacteristic
193C22×C157#12011yescharacteristic
194C22×C157#12111yescharacteristic
195C22×C157#12111yescharacteristic
196C22×C157#12111yescharacteristic
197C22×C157#12111yescharacteristic
198C22×C157#12111yescharacteristic
199C22×C157#12111yescharacteristic
200C22×C157#12111yescharacteristic
201C22×C157#12111yescharacteristic
202C22×C157C22⋊Q811yescharacteristic
203C22×C157C22⋊Q811yescharacteristic
204C22×C157C22⋊Q811yescharacteristic
205C22×C157C22⋊Q811yescharacteristic
206C22×C157C22⋊Q811yescharacteristic
207C22×C157C22⋊Q811yescharacteristic
208C22×C157#12311yescharacteristic
209C22×C157#12311yescharacteristic
210C22×C157#12311yescharacteristic
211C22×C157#12311yescharacteristic
212C22×C157#12311yescharacteristic
213C22×C157#12411yescharacteristic
214C22×C157#12411yescharacteristic
215C22×C157#12411yescharacteristic
216C22×C157#12611yescharacteristic
217C22×C157#12611yescharacteristic
218C22×C157#12711yescharacteristic
219C2×D157—24no—
220C2×D157—24no—
221C2×D157—24no—
222C2×D157—42no—
223C2×D157—42no—
224C2×D157—42no—
225C2×D157—42no—
226C2×D157—42no—
227C2×D157—42no—
228C2×D157—42no—
229C2×D157—42no—
230C2×D157—42no—
231C2×D157—42no—
232C2×D157—42no—
233C2×D157—42no—
234C4×C157—42no—
235C4×C157—42no—
236C4×C157—42no—
237Dic157—24no—
238Dic157—42no—
239Dic157—42no—
240C2×C157#38011yescharacteristic
241C2×C157#38511yescharacteristic
242C2×C157#38511yescharacteristic
243C2×C157#38611yescharacteristic
244C2×C157#38811yescharacteristic
245C2×C157#38811yescharacteristic
246C2×C157#39011yescharacteristic
247C2×C157#39211yescharacteristic
248C2×C157#39311yescharacteristic
249C2×C157#39411yescharacteristic
250C2×C157#39411yescharacteristic
251C2×C157#39611yescharacteristic
252C2×C157#39611yescharacteristic
253C2×C157#39711yescharacteristic
254C2×C157#39911yescharacteristic
255D157—44no—
256C157#143911yescharacteristic, complemented, Sylow
257#1439—1571nomaximal, Sylow
258C22×C4⋊C4—1571no—
259C22×C22⋊C4—1571no—
260C22×C22⋊C4—1571no—
261C22×C22⋊C4—1571no—
262C2×#95—1571no—
263C2×#95—1571no—
264C2×#95D15711yescharacteristic, complemented
265C25—1571no—
266C23×C4—1571no—
267C23×C4—1571no—
268C23×C4—1571no—
269C23×C4C2×D15711yescharacteristic
270C23×C4C2×D15711yescharacteristic
271C23×C4C2×D15711yescharacteristic
272C2×C4⋊C4—3142no—
273C2×C4⋊C4—3142no—
274C2×C4⋊C4—3142no—
275C2×C22⋊C4—3142no—
276C2×C22⋊C4—3142no—
277C2×C22⋊C4—3142no—
278C2×C22⋊C4—3142no—
279C2×C22⋊C4—3142no—
280C2×C22⋊C4—3142no—
281C2×C22⋊C4—3142no—
282C2×C22⋊C4—3142no—
283C2×C22⋊C4—1574no—
284#95—22no—
285#95—3142no—
286#95—3142no—
287C24—3141no—
288C24—3141no—
289C24—3141no—
290C24—3141no—
291C24—3141no—
292C24—3141no—
293C24—3141no—
294C24—3141no—
295C24—3141no—
296C24—3141no—
297C24—3141no—
298C24—3141no—
299C24—1572no—
300C24—1572no—
301C24—1572no—
302C24C22×D15711yescharacteristic
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—3141no—
322C22×C4—3141no—
323C22×C4—3141no—
324C22×C4—3141no—
325C22×C4—3141no—
326C22×C4—3141no—
327C22×C4—3141no—
328C22×C4—3141no—
329C22×C4—3141no—
330C22×C4—3141no—
331C22×C4—3141no—
332C22×C4—3141no—
333C22×C4—3141no—
334C22×C4—3141no—
335C22×C4—3141no—
336C22×C4—3141no—
337C22×C4—1572no—
338C22×C4—1572no—
339C22×C4—1572no—
340C22×C4—1572no—
341C22×C4—1572no—
342C22×C4C4×D15712yes—
343C22×C4C22⋊D15712yes—
344C22×C4D62812yes—
345C4⋊C4—3148no—
346C22⋊C4—3148no—
347C22⋊C4—3148no—
348C22⋊C4—3148no—
349C23—3142no—
350C23—3142no—
351C23—3142no—
352C23—3142no—
353C23—3142no—
354C23—3142no—
355C23—3142no—
356C23—3142no—
357C23—3142no—
358C23—3142no—
359C23—3142no—
360C23—3142no—
361C23—3142no—
362C23—3142no—
363C23—3142no—
364C23—3142no—
365C23—3142no—
366C23—3142no—
367C23—6281no—
368C23—6281no—
369C23—6281no—
370C23—6281no—
371C23—6281no—
372C23—6281no—
373C23—6281no—
374C23—6281no—
375C23—6281no—
376C23—6281no—
377C23—6281no—
378C23—6281no—
379C23—6281no—
380C23—6281no—
381C23—6281no—
382C23—6281no—
383C23—1574no—
384C23C2×C4×D15711yescharacteristic
385C23D4×D15711yescharacteristic
386C23D4×D15711yescharacteristic
387C23D4×D15711yescharacteristic
388C23D4×D15711yescharacteristic
389C23D4×D15711yescharacteristic
390C23C2×C22⋊D15711yescharacteristic
391C23C2×D62811yescharacteristic
392C23Q8×D15711yescharacteristic
393C23#1457895311yescharacteristic
394C23#1457895411yescharacteristic
395C23#1457895411yescharacteristic
396C23#1457895411yescharacteristic
397C23#1457895411yescharacteristic
398C23#1457895511yescharacteristic
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—3142no—
421C2×C4—3142no—
422C2×C4—3142no—
423C2×C4—3142no—
424C2×C4—3142no—
425C2×C4—3142no—
426C2×C4—3142no—
427C2×C4—3142no—
428C2×C4—3142no—
429C2×C4—3142no—
430C2×C4—3142no—
431C2×C4—3142no—
432C2×C4—6281no—
433C2×C4—6281no—
434C2×C4—6281no—
435C2×C4—6281no—
436C2×C4—6281no—
437C2×C4—6281no—
438C2×C4—6281no—
439C2×C4—6281no—
440C2×C4—1574no—
441C22—3144no—
442C22—3144no—
443C22—3144no—
444C22—6282no—
445C22—6282no—
446C22—6282no—
447C22—6282no—
448C22—6282no—
449C22—6282no—
450C22—6282no—
451C22—6282no—
452C22—6282no—
453C22—6282no—
454C22—6282no—
455C22—6282no—
456C22C22⋊C4×D15711yescharacteristic
457C22C4⋊C4×D15711yescharacteristic
458C22#1909772811yescharacteristic
459C22#1909773111yescharacteristic
460C22C4×C22⋊D15711yescharacteristic
461C22#1909773311yescharacteristic
462C22C4×D62811yescharacteristic
463C22#1909773911yescharacteristic
464C22#1909774111yescharacteristic
465C22#1909774111yescharacteristic
466C22#1909774311yescharacteristic
467C22#1909774411yescharacteristic
468C22#1909774411yescharacteristic
469C22#1909774411yescharacteristic
470C22#1909774411yescharacteristic
471C22#1909774411yescharacteristic
472C22#1909774511yescharacteristic
473C22#1909774611yescharacteristic
474C22#1909774711yescharacteristic
475C22#1909774911yescharacteristic
476C22#1909774911yescharacteristic
477C22#1909774911yescharacteristic
478C22#1909774911yescharacteristic
479C22#1909775111yescharacteristic
480C22#1909775311yescharacteristic
481C22#1909775411yescharacteristic
482C22#1909775611yescharacteristic
483C22#1909775611yescharacteristic
484C22#1909775611yescharacteristic
485C22#1909775711yescharacteristic
486C22#1909775711yescharacteristic
487C22#1909775911yescharacteristic
488C22#1909776511yescharacteristic
489C22#1909776611yescharacteristic
490C22#1909776711yescharacteristic
491C4—42no—
492C4—42no—
493C4—42no—
494C4—3144no—
495C4—6282no—
496C4—6282no—
497C2—6284no—
498C2#2375713211yescharacteristic
499C2#2375714411yescharacteristic
500C2#2375714711yescharacteristic
501C2#2375715111yescharacteristic
502C2#2375716211yescharacteristic
503C2#2375716411yescharacteristic
504C2#2375717311yescharacteristic
505C2#2375718211yescharacteristic
506C2#2375718611yescharacteristic
507C2#2375718811yescharacteristic
508C2#2375719111yescharacteristic
509C2#2375719511yescharacteristic
510C2#2375719711yescharacteristic
511C2#2375720211yescharacteristic
512C2#2375720811yescharacteristic
subgroupG/H
center, FrattiniC24C22×D157
commutatorC23×C157C22×C4
FittingC2×#95×C157C2
socle, cosocleC24×C157C23
prime radicalC24×D157C22
hypercenterC2×#95D157
hypocenterC157#1439
LCSG ▷ C23×C157 ▷ C157
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
1. C22×#14578933C2semidirect
5. C2×#19097678C2semidirect
6. C2×#19097678C2semidirect
7. C2×#95×C157C2semidirect
23. C2×#14578931C4semidirect
126. C22×D157C4⋊C4semidirect
147. C2×Dic157C22⋊C4semidirect
256. C157#1439semidirect
264. C2×#95D157semidirect

Maximal subgroups

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

subgroupindex
C22×#145789332
C22×#145789312
C2×#190976782
C2×#95×C1572
#1439157