Finite Group Databasebeta

← #29595987

Subgroups — #29595987

Order 15616.

600 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 103 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#21448473C211yesmaximal, characteristic
2C2×#16839550C212yesmaximal
3#21445807C211yesmaximal, characteristic, complemented
4#21443938C212yesmaximal, complemented
5C61×#1800C211yesmaximal, characteristic, complemented
6C2×#14519745C2211yescharacteristic
7C22×#11758198C411yescharacteristic, complemented
8C2×#14519692C2212yes—
9#16839662—21no—
10#16839653—21no—
11#16839652—21no—
12#16839642C2211yescharacteristic
13#16839641—21no—
14#16839634C411yescharacteristic, complemented
15#16839622—21no—
16#16839617C411yescharacteristic, complemented
17C4×C22⋊Dic61C411yescharacteristic, complemented
18#16839550—24no—
19#16839529—21no—
20C2×C4×D4×C61C2211yescharacteristic
21C61×#423—21no—
22C2×#100×C61C2212yes—
23C61×#343—21no—
24C24×D61C2×C411yescharacteristic
25C22×C22⋊D61—21no—
26C23×Dic61C2×C411yescharacteristic
27#14519745—21no—
28#14519745—21no—
29#14519745D412yes—
30#14519745Q812yes—
31C2×C4⋊Dic61—41no—
32C2×#11758196—21no—
33C2×C22⋊Dic61—22no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61C2×C411yescharacteristic
36C2×C22⋊Dic61C2×C411yescharacteristic
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—41no—
43C2×#11758198—41no—
44C2×C4×Dic61—21no—
45#14519692—22no—
46#14519692—22no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—41no—
51C22×D4×C61C2311yescharacteristic
52C23×C4×C61C2×C411yescharacteristic
53C23×C4×C61D411yescharacteristic
54C2×M16×C61—22no—
55C4×D4×C61—41no—
56C4×D4×C61—41no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C22⋊C4×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61D411yescharacteristic
60C2×C42×C61D411yescharacteristic
61C4⋊C8×C61—41no—
62C4⋊C8×C61—41no—
63#100×C61—22no—
64#100×C61—22no—
65C24×C61C22×C411yescharacteristic
66C24×C61C2×D411yescharacteristic
67C23×D61—21no—
68C23×D61—21no—
69C23×D61—41no—
70C23×D61—41no—
71C23×D61—81no—
72C23×D61—81no—
73C23×D61C4⋊C412yescomplemented
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61C2×D411yescharacteristic
77C2×D4×C61C2×Q811yescharacteristic
78C2×D4×C61#4111yescharacteristic
79C2×D4×C61#4111yescharacteristic
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—81no—
85C22×C4×C61—81no—
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C22⋊C411yescharacteristic
89C22×C4×C61C22⋊C411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C2×C22⋊D61—22no—
92C2×C22⋊D61—22no—
93C2×C22⋊D61—81no—
94C2×C22⋊D61—81no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—41no—
99C22×Dic61—42no—
100C22×Dic61—81no—
101M16×C61—42no—
102M16×C61—42no—
103C2×C8×C61—42no—
104C4⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C42×C61—21no—
108C42×C61—21no—
109C22⋊Dic61—21no—
110C22⋊Dic61—41no—
111C22⋊Dic61—42no—
112C22⋊Dic61—42no—
113C22⋊Dic61—81no—
114C22⋊Dic61C4⋊C412yescomplemented
115#11758198—22no—
116#11758198—22no—
117#11758198—42no—
118#11758198—41no—
119#11758198—41no—
120#11758198—81no—
121#11758198—81no—
122C4⋊Dic61—82no—
123#11758196—81no—
124C4×Dic61—81no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61C2×C22⋊C411yescharacteristic
134C23×C61C2×C4⋊C411yescharacteristic
135C23×C61#11711yescharacteristic
136C23×C61#12111yescharacteristic
137C23×C61C22⋊Q811yescharacteristic
138C22×D61—22no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—42no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—42no—
147C22×D61—82no—
148C22×D61—82no—
149C22×D61—84no—
150C22×D61—82no—
151C22×D61—82no—
152D4×C61—41no—
153D4×C61—41no—
154D4×C61—41no—
155D4×C61—41no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—41no—
162C2×C4×C61—42no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—81no—
167C2×C4×C61—81no—
168C2×C4×C61—81no—
169C2×C4×C61#9911yescharacteristic
170C2×C4×C61#9911yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61C22⋊Q811yescharacteristic
173C22⋊D61—82no—
174C22⋊D61—82no—
175C2×Dic61—22no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—82no—
185C2×Dic61—82no—
186C2×Dic61—82no—
187C2×Dic61—82no—
188C8×C61—82no—
189#12795—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—42no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61—81no—
206C22×C61#38011yescharacteristic
207C22×C61C2×#9911yescharacteristic
208C22×C61#41011yescharacteristic
209C2×D61—42no—
210C2×D61—42no—
211C2×D61—42no—
212C2×D61—81no—
213C2×D61—81no—
214C2×D61—84no—
215C2×D61—81no—
216C2×D61—81no—
217C2×D61—84no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—41no—
223C4×C61—41no—
224C4×C61—41no—
225Dic61—42no—
226Dic61—81no—
227Dic61—81no—
228Dic61—162no—
229#2321—611no—
230C2×AΣL(1,𝔽16)—612no—
231#1800D6111yescharacteristic, complemented
232#1799—611no—
233#1390—612no—
234C2×C61—21no—
235C2×C61—21no—
236C2×C61—41no—
237C2×C61—41no—
238C2×C61—41no—
239C2×C61—41no—
240C2×C61#179911yescharacteristic
241C2×C61#212111yescharacteristic
242C2×C61#212211yescharacteristic
243D61—82no—
244C2×#120—611no—
245C2×C4×D4C2×D6111yescharacteristic
246C22×C22⋊C4—611no—
247#423—21no—
248C2×#100C2×D6112yes—
249C2×#99—612no—
250#390—1221no—
251#388—1221no—
252#388—1221no—
253#386—611no—
254#386—1221no—
255#385—611no—
256#380—1221no—
257#379—611no—
258C4×C22⋊C4—611no—
259AΣL(1,𝔽16)—1224no—
260#343—21no—
261#342—1221no—
262C61#1279511yescharacteristic, complemented, Sylow
263C25—611no—
264C22×D4—1221no—
265C22×D4C22×D6111yescharacteristic
266C23×C4—611no—
267C23×C4C4×D6111yescharacteristic
268C23×C4D24411yescharacteristic
269C2×M16—22no—
270#120—612no—
271#120—612no—
272#120—1221no—
273#120—1221no—
274C4×D4—41no—
275C4×D4—41no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4—2441no—
278C2×C4⋊C4C22⋊D6111yescharacteristic
279C2×C22⋊C4—611no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—1221no—
282C2×C22⋊C4—1221no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—1221no—
286C2×C22⋊C4—1221no—
287C2×C22⋊C4—1222no—
288C2×C22⋊C4—2441no—
289C2×C22⋊C4—2441no—
290C2×C22⋊C4C4×D6111yescharacteristic
291C2×C22⋊C4D24411yescharacteristic
292C2×C42—1221no—
293C2×C42C22⋊D6111yescharacteristic
294C4⋊C8—41no—
295C4⋊C8—41no—
296#100—22no—
297#100—22no—
298#99—1222no—
299#99—1222no—
300#95—1221no—
301#95—1221no—
302#95—1221no—
303#95—2441no—
304C24—612no—
305C24—1221no—
306C24—1221no—
307C24—4881no—
308C24—4881no—
309C24—2441no—
310C24—2441no—
311C24C2×C4×D6111yescharacteristic
312C24C2×D24411yescharacteristic
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—1222no—
316C2×D4—1222no—
317C2×D4—4881no—
318C2×D4—4881no—
319C2×D4D4×D6111yescharacteristic
320C2×D4#1175822411yescharacteristic
321C2×D4Q8×D6111yescharacteristic
322C2×D4#1175822611yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—81no—
328C22×C4—81no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—4881no—
333C22×C4—2442no—
334C22×C4—2441no—
335C22×C4#1175819811yescharacteristic
336C22×C4#1175819811yescharacteristic
337C22×C4#1175819811yescharacteristic
338C22×C4#1175819811yescharacteristic
339C22×C4C2×C22⋊D6111yescharacteristic
340M16—42no—
341M16—42no—
342C2×C8—42no—
343C4⋊C4—41no—
344C4⋊C4—4882no—
345C4⋊C4—4881no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—612no—
349C22⋊C4—1221no—
350C22⋊C4—1222no—
351C22⋊C4—1222no—
352C22⋊C4—4881no—
353C22⋊C4—4881no—
354C22⋊C4—4881no—
355C22⋊C4—2442no—
356C22⋊C4—2442no—
357C22⋊C4—2442no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C42—21no—
362C42—21no—
363C42—4881no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—1222no—
373C23—4882no—
374C23—4882no—
375C23—4884no—
376C23—4882no—
377C23—4882no—
378C23—2442no—
379C23—2441no—
380C23—2441no—
381C23—2441no—
382C23—2441no—
383C23—2442no—
384C23—2441no—
385C23—2441no—
386C23C2×#1175819811yescharacteristic
387C23C4⋊C4×D6111yescharacteristic
388C23#1451973511yescharacteristic
389C23#1451975211yescharacteristic
390C23#1451975711yescharacteristic
391D4—41no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—4882no—
396D4—4882no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—1222no—
411C2×C4—4882no—
412C2×C4—4882no—
413C2×C4—4882no—
414C2×C4—4882no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4#1451969111yescharacteristic
424C2×C4#1451969111yescharacteristic
425C2×C4#1451974811yescharacteristic
426C2×C4#1451975311yescharacteristic
427C8—82no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—42no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—81no—
444C22—4881no—
445C22—4881no—
446C22—4884no—
447C22—4884no—
448C22—4881no—
449C22—4881no—
450C22—2442no—
451C22—2442no—
452C22—2442no—
453C22#1683961911yescharacteristic
454C22C2×#1451969111yescharacteristic
455C22#1683973511yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—41no—
461C4—41no—
462C4—41no—
463C4—9762no—
464C4—4881no—
465C4—4881no—
466C4—2442no—
467C2—21no—
468C2—21no—
469C2—41no—
470C2—41no—
471C2—41no—
472C2—41no—
473C2—4882no—
474C2#2144580411yescharacteristic
475C2#2144746611yescharacteristic
476C2#2144747011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC24×C61C22×C4
FrattiniC22×D4C22×D61
FittingC61×#1800C2
socleC22×C61C2×#99
prime radicalC2×#14519745C22
cosocleC22×D4×C61C23
hypercenter#1800D61
hypocenterC61#12795
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #21445807C2semidirect
4. #21443938C2semidirect
5. C61×#1800C2semidirect
7. C22×#11758198C4semidirect
14. #16839634C4semidirect
16. #16839617C4semidirect
17. C4×C22⋊Dic61C4semidirect
73. C23×D61C4⋊C4semidirect
114. C22⋊Dic61C4⋊C4semidirect
231. #1800D61semidirect
262. C61#12795semidirect

Maximal subgroups

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

subgroupindex
#214484732
C2×#168395502
#214458072
#214439382
C61×#18002
#1279561