Finite Group Databasebeta

← #28489257

Subgroups — #28489257

Order 15104.

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

normal subgroups only

This group has 658 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×#16837720C211yesmaximal, characteristic
2#21430030C211yesmaximal, characteristic
3C2×#16837139C211yesmaximal, characteristic, complemented
4C2×#16837137C211yesmaximal, characteristic
5#21422364C211yesmaximal, characteristic, complemented
6#21421938C211yesmaximal, characteristic, complemented
7C2×C59×#484C211yesmaximal, characteristic, complemented
8C2×#14273701C2211yescharacteristic
9#16837720—22no—
10#16837720—22no—
11C2×#14273658—21no—
12C2×#14273647—21no—
13C2×C22⋊(C59⋊C8)C2211yescharacteristic
14#16837341—21no—
15#16837328—21no—
16#16837319—21no—
17#16837313—21no—
18#16837279—22no—
19C2×C59⋊#95—22no—
20C2×C59⋊#95C2211yescharacteristic
21C2×C59⋊#95C2211yescharacteristic
22#16837139—22no—
23#16837137—22no—
24C2×C22⋊Q8×C59C2211yescharacteristic
25C22×C4⋊C4×C59C2211yescharacteristic
26C59×#484—22no—
27C59×#484—22no—
28C2×#107×C59—21no—
29C2×#103×C59—21no—
30C2×C22⋊C8×C59C2211yescharacteristic
31C22×D236D411yescharacteristic
32C22×C22⋊D59—21no—
33C23×Dic59—21no—
34C23×Dic59D412yes—
35C22×C59⋊C8—21no—
36#14273701—21no—
37#14273701—21no—
38#14273701—21no—
39#14273701—21no—
40C2×C4⋊Dic59D411yescharacteristic
41C2×(C2×D59)⋊C4—21no—
42C2×(C2×D59)⋊C4—22no—
43C2×(C2×D59)⋊C4—22no—
44#14273658—24no—
45#14273647—24no—
46C22⋊(C59⋊C8)—21no—
47C22⋊(C59⋊C8)D412yes—
48C59⋊#95—22no—
49C59⋊#95—22no—
50C59⋊#95—21no—
51C59⋊#95—21no—
52C59⋊#95—21no—
53C59⋊#95—21no—
54C59⋊#95—44no—
55C22×Q8×C59D411yescharacteristic
56C23×C4×C59—21no—
57C23×C4×C59C2311yescharacteristic
58C22×C8×C59—21no—
59C22⋊Q8×C59—21no—
60C22⋊Q8×C59—21no—
61C22⋊Q8×C59—21no—
62C22⋊Q8×C59—21no—
63C2×C4⋊C4×C59—21no—
64C2×C4⋊C4×C59—21no—
65C2×C4⋊C4×C59—21no—
66C2×C4⋊C4×C59—21no—
67C2×C4⋊C4×C59—21no—
68C2×C4⋊C4×C59—21no—
69C2×C4⋊C4×C59D412yes—
70C2×C4⋊C4×C59D411yescharacteristic
71C2×C22⋊C4×C59—21no—
72#107×C59—24no—
73#103×C59—24no—
74C22⋊C8×C59—21no—
75C22⋊C8×C59D412yes—
76C24×C59C2×D411yescharacteristic
77C23×D59—21no—
78C2×Q8×C59—21no—
79C2×Q8×C59—21no—
80C2×Q8×C59—42no—
81C22×C4×C59—21no—
82C22×C4×C59—21no—
83C22×C4×C59—22no—
84C22×C4×C59—42no—
85C22×C4×C59—42no—
86C22×C4×C59—42no—
87C22×C4×C59—41no—
88C22×C4×C59—41no—
89C22×C4×C59C2×D411yescharacteristic
90C22×C4×C59C2×D411yescharacteristic
91C22×C4×C59C2×D411yescharacteristic
92C22×C4×C59C2×D411yescharacteristic
93C22×C4×C59C2×D411yescharacteristic
94C22×C4×C59#4111yescharacteristic
95C2×C22⋊D59—41no—
96C2×C22⋊D59—41no—
97C2×C22⋊D59—42no—
98C2×C22⋊D59—42no—
99C22×Dic59—22no—
100C22×Dic59—22no—
101C22×Dic59—21no—
102C22×Dic59—22no—
103C22×Dic59—22no—
104C22×Dic59—42no—
105C22×Dic59—42no—
106C22×Dic59—41no—
107C22×Dic59—42no—
108C22×Dic59—41no—
109C22×Dic59—42no—
110C2×D236—21no—
111C2×D236—21no—
112C2×D236—42no—
113C2×C8×C59—22no—
114C2×C8×C59—42no—
115C4⋊C4×C59—22no—
116C4⋊C4×C59—21no—
117C4⋊C4×C59—22no—
118C4⋊C4×C59—21no—
119C4⋊C4×C59—41no—
120C4⋊C4×C59—41no—
121C4⋊C4×C59—41no—
122C4⋊C4×C59—41no—
123C22⋊C4×C59—41no—
124C22⋊C4×C59—41no—
125(C2×D59)⋊C4—41no—
126(C2×D59)⋊C4—41no—
127(C2×D59)⋊C4—82no—
128(C2×D59)⋊C4—82no—
129C4⋊Dic59—21no—
130C4⋊Dic59—21no—
131C2×C59⋊C8—22no—
132C2×C59⋊C8—42no—
133C23×C59—21no—
134C23×C59—21no—
135C23×C59—22no—
136C23×C59#12011yescharacteristic
137C23×C59#12111yescharacteristic
138C23×C59#12711yescharacteristic
139C23×C59#13512yes—
140C23×C59#13712yes—
141C22×D59—41no—
142C22×D59—42no—
143C22×D59—41no—
144C22×D59—41no—
145C22×D59—42no—
146Q8×C59—42no—
147Q8×C59—81no—
148C2×C4×C59—22no—
149C2×C4×C59—22no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59—41no—
153C2×C4×C59—41no—
154C2×C4×C59—44no—
155C2×C4×C59—41no—
156C2×C4×C59—41no—
157C2×C4×C59—42no—
158C2×C4×C59—41no—
159C2×C4×C59—41no—
160C2×C4×C59—42no—
161C2×C4×C59—82no—
162C2×C4×C59—81no—
163C2×C4×C59—81no—
164C2×C4×C59#12011yescharacteristic
165C2×C4×C59#12011yescharacteristic
166C2×C4×C59#12111yescharacteristic
167C2×C4×C59#12111yescharacteristic
168C22⋊D59—82no—
169C22⋊D59—81no—
170C22⋊D59—81no—
171C2×Dic59—44no—
172C2×Dic59—42no—
173C2×Dic59—44no—
174C2×Dic59—41no—
175C2×Dic59—42no—
176C2×Dic59—42no—
177C2×Dic59—42no—
178C2×Dic59—42no—
179C2×Dic59—82no—
180C2×Dic59—81no—
181C2×Dic59—81no—
182C2×Dic59—82no—
183D236—42no—
184D236—81no—
185C8×C59—42no—
186C59⋊C8—42no—
187#9969—591nomaximal, Sylow
188C22×C59—22no—
189C22×C59—22no—
190C22×C59—22no—
191C22×C59—22no—
192C22×C59—21no—
193C22×C59—21no—
194C22×C59—21no—
195C22×C59—21no—
196C22×C59#39211yescharacteristic
197C22×C59#45212yes—
198C22×C59#45311yescharacteristic
199C22×C59#45411yescharacteristic
200C22×C59#45812yes—
201C22×C59#46412yes—
202C22×C59#49511yescharacteristic
203C22×C59#49711yescharacteristic
204C2×D59—82no—
205C2×D59—82no—
206C2×D59—81no—
207C2×D59—81no—
208C2×D59—81no—
209C4×C59—21no—
210C4×C59—21no—
211C4×C59—21no—
212C4×C59—21no—
213C4×C59—81no—
214C4×C59—82no—
215C4×C59—81no—
216Dic59—82no—
217Dic59—82no—
218Dic59—81no—
219C2×#484D5911yescharacteristic, complemented
220C2×#481—591no—
221#2639—591no—
222C2×#328—591no—
223C2×#327—591no—
224#1445—591no—
225#1280—591no—
226C2×C59—21no—
227C2×C59—22no—
228C2×C59—21no—
229C2×C59#161512yes—
230C2×C59#161812yes—
231C2×C59#200611yescharacteristic
232C2×C59#201511yescharacteristic
233C2×C59#202211yescharacteristic
234D59—161no—
235C2×C22⋊Q8C2×D5911yescharacteristic
236C2×#121—591no—
237C22×C4⋊C4C2×D5911yescharacteristic
238#484—22no—
239#484—22no—
240#481—1182no—
241#481—1182no—
242C2×#107—21no—
243C2×#106—1181no—
244C2×#103—21no—
245C2×#102—1181no—
246C2×C22⋊C8—591no—
247C2×C22⋊C8C2×D5911yescharacteristic
248#400—1181no—
249#397—1181no—
250#394—1181no—
251#393—1181no—
252#386—1182no—
253C2×#95—591no—
254C2×#95—591no—
255C2×#95—1182no—
256#328—1182no—
257#327—1182no—
258C59#996911yescharacteristic, complemented, Sylow
259C22×Q8C22⋊D5911yescharacteristic
260C22×D4—591no—
261C22×D4—1181no—
262C23×C4—21no—
263C23×C4—592no—
264C23×C4—1181no—
265C23×C4C22×D5911yescharacteristic
266C22×C8—21no—
267C22×C8—1181no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272#121—1181no—
273#121—1181no—
274#121—1181no—
275#121—1181no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—591no—
283C2×C4⋊C4C22⋊D5912yes—
284C2×C4⋊C4C22⋊D5911yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—1182no—
287C2×C22⋊C4—1182no—
288C2×C22⋊C4—1181no—
289#107—24no—
290#106—1184no—
291#103—24no—
292#102—1184no—
293C22⋊C8—21no—
294C22⋊C8—592no—
295C22⋊C8—1181no—
296C22⋊C8C22⋊D5912yes—
297#95—1182no—
298#95—1182no—
299#95—1181no—
300#95—1181no—
301#95—1181no—
302#95—1181no—
303#95—2364no—
304C24—1181no—
305C24D4×D5911yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—42no—
309C2×D4—1181no—
310C2×D4—1181no—
311C2×D4—2362no—
312C2×D4—2361no—
313C2×D4—2361no—
314C2×D4—2362no—
315C2×D4—2362no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—1182no—
325C22×C4—1182no—
326C22×C4—1182no—
327C22×C4—1181no—
328C22×C4—1182no—
329C22×C4—2361no—
330C22×C4—2362no—
331C22×C4—2361no—
332C22×C4—2362no—
333C22×C4—2362no—
334C22×C4—2362no—
335C22×C4D4×D5911yescharacteristic
336C22×C4D4×D5911yescharacteristic
337C22×C4#1174568711yescharacteristic
338C22×C4C2×C22⋊D5911yescharacteristic
339C22×C4C2×C22⋊D5911yescharacteristic
340C22×C4C2×C22⋊D5911yescharacteristic
341C2×C8—22no—
342C2×C8—42no—
343C2×C8—1182no—
344C2×C8—2362no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—1181no—
354C4⋊C4—1181no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—4722no—
358C22⋊C4—4722no—
359C22⋊C4—2361no—
360C22⋊C4—2361no—
361C23—21no—
362C23—21no—
363C23—22no—
364C23—2362no—
365C23—2361no—
366C23—2361no—
367C23—2361no—
368C23—2362no—
369C23#1427369511yescharacteristic
370C23#1427369911yescharacteristic
371C23#1427372311yescharacteristic
372C23#1427375012yes—
373C23#1427375912yes—
374Q8—42no—
375Q8—81no—
376D4—4721no—
377D4—4721no—
378D4—4721no—
379D4—4722no—
380D4—2362no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—44no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—82no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—4722no—
398C2×C4—4721no—
399C2×C4—4721no—
400C2×C4—4722no—
401C2×C4—2364no—
402C2×C4—2362no—
403C2×C4—2364no—
404C2×C4—2362no—
405C2×C4—2362no—
406C2×C4—2361no—
407C2×C4—2362no—
408C2×C4—2362no—
409C2×C4#1427369511yescharacteristic
410C2×C4#1427369611yescharacteristic
411C2×C4#1427369811yescharacteristic
412C2×C4#1427369911yescharacteristic
413C8—42no—
414C8—2362no—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—4722no—
424C22—4721no—
425C22—4722no—
426C22—4721no—
427C22—4721no—
428C22#1683731011yescharacteristic
429C22#1683756312yes—
430C22#1683756811yescharacteristic
431C22#1683757311yescharacteristic
432C22#1683759112yes—
433C22#1683762612yes—
434C22#1683778711yescharacteristic
435C22#1683779511yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—81no—
441C4—82no—
442C4—81no—
443C4—4722no—
444C4—4721no—
445C4—4722no—
446C2—21no—
447C2—21no—
448C2—22no—
449C2—9441no—
450C2#2142312612yes—
451C2#2142314312yes—
452C2#2142513611yescharacteristic
453C2#2142518711yescharacteristic
454C2#2142522411yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC2×C59×#484C2
socleC23×C59#120
prime radicalC2×#14273701C22
hypercenterC2×#484D59
hypocenterC59#9969
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. C2×#16837139C2semidirect
5. #21422364C2semidirect
6. #21421938C2semidirect
7. C2×C59×#484C2semidirect
219. C2×#484D59semidirect
258. C59#9969semidirect

Maximal subgroups

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

subgroupindex
C2×#168377202
#214300302
C2×#168371392
C2×#168371372
#214223642
#214219382
C2×C59×#4842
#996959