Finite Group Databasebeta

← #29590776

Subgroups — #29590776

Order 15616.

582 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 71 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#21449097C211yesmaximal, characteristic
2#21445806C211yesmaximal, characteristic, complemented
3#21444154C211yesmaximal, characteristic, complemented
4#21443844C211yesmaximal, characteristic, complemented
5#21443842C211yesmaximal, characteristic, complemented
6#21443816C211yesmaximal, characteristic, complemented
7C61×#1343C211yesmaximal, characteristic, complemented
8C2×D4×Dic61—21no—
9C2×D4×Dic61C411yescharacteristic, complemented
10C2×#14519737—21no—
11C2×#14519737C2211yescharacteristic
12C2×#14519691—21no—
13#16839724—21no—
14#16839699C411yescharacteristic, complemented
15#16839698—21no—
16#16839698C2211yescharacteristic
17#16839670—21no—
18#16839670C411yescharacteristic, complemented
19#16839620—21no—
20#16839607C411yescharacteristic, complemented
21#16839529C2211yescharacteristic
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#392C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61—21no—
28C22×C22⋊D61D411yescharacteristic
29C23×Dic61—21no—
30C23×Dic61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×#11758189—41no—
33D4×Dic61—44no—
34D4×Dic61—41no—
35D4×Dic61—41no—
36#14519737—41no—
37#14519737—41no—
38#14519737—44no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—41no—
43C2×#11758196D411yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×#11758198—21no—
49C2×#11758198C2×C411yescharacteristic
50C2×C4×Dic61—21no—
51C2×C4×Dic61C2×C411yescharacteristic
52#14519691—42no—
53C22⋊#92418—21no—
54#14519689—41no—
55#14519684—21no—
56#14519684—41no—
57#14519684C2×C411yescharacteristic
58C22×D4×C61—21no—
59C22×D4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61C2311yescharacteristic
63C22⋊C8×C61—21no—
64#95×C61C2×C411yescharacteristic
65C24×C61—21no—
66C24×C61C2×D411yescharacteristic
67C23×D61C22⋊C411yescharacteristic
68C2×D4×C61—42no—
69C2×D4×C61—41no—
70C2×D4×C61—42no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—42no—
74C22×C4×C61—21no—
75C22×C4×C61—41no—
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C2×C22⋊D61—21no—
79C2×C22⋊D61—21no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—42no—
83C2×C22⋊D61—42no—
84C2×C22⋊D61—42no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—42no—
90C22×Dic61—42no—
91C22×Dic61—42no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94C22×Dic61—41no—
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C22×Dic61C22⋊C411yescharacteristic
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—42no—
101C2×C8×C61—41no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—42no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊Dic61—42no—
107C22⋊Dic61—42no—
108C22⋊Dic61—42no—
109C22⋊Dic61—41no—
110C22⋊Dic61—41no—
111#11758198—41no—
112#11758198—42no—
113C4⋊Dic61—42no—
114C4⋊Dic61—41no—
115#11758196—41no—
116#11758196—42no—
117#11758196—82no—
118C4×Dic61—24no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C2×#92418—41no—
122#11758189—82no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—22no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61C2×C22⋊C411yescharacteristic
135C23×C61AGL(1,ℤ/8)11yescharacteristic
136C23×C61#13711yescharacteristic
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—41no—
141C22×D61—41no—
142D4×C61—42no—
143D4×C61—44no—
144D4×C61—44no—
145D4×C61—42no—
146C2×C4×C61—22no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—81no—
154C2×C4×C61—81no—
155C2×C4×C61—81no—
156C22⋊D61—42no—
157C22⋊D61—42no—
158C22⋊D61—48no—
159C2×Dic61—22no—
160C2×Dic61—22no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—42no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—81no—
173C2×Dic61—82no—
174C2×Dic61—82no—
175C2×Dic61—81no—
176C2×Dic61—81no—
177C2×Dic61—81no—
178C2×Dic61#9911yescharacteristic
179C2×Dic61#9911yescharacteristic
180C4×D61—42no—
181C4×D61—81no—
182C8×C61—81no—
183#92418—81no—
184#11821—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—42no—
192C22×C61—42no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61—42no—
196C22×C61—81no—
197C22×C61—81no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61C2×#9911yescharacteristic
202C22×C61#41711yescharacteristic
203C22×C61#42111yescharacteristic
204C2×D61—42no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—81no—
209C4×C61—42no—
210C4×C61—41no—
211C4×C61—41no—
212C4×C61—161no—
213Dic61—21no—
214Dic61—42no—
215Dic61—41no—
216Dic61—41no—
217Dic61—81no—
218Dic61—161no—
219Dic61#35312yes—
220#2397—611no—
221#1799—611no—
222#1465—611no—
223#1352—611no—
224#1352—611no—
225#1343—611no—
226#1343D6111yescharacteristic, complemented
227C2×C61—21no—
228C2×C61—21no—
229C2×C61—41no—
230C2×C61—41no—
231C2×C61—82no—
232C2×C61#151311yescharacteristic
233C2×C61#212011yescharacteristic
234C2×C61C2×#35311yescharacteristic
235D61—81no—
236C2×C4×D4—611no—
237C2×C4×D4—611no—
238C2×C4×D4—1221no—
239C2×C4×D4—1221no—
240C2×#99—1221no—
241#407—1221no—
242#399—611no—
243#399—611no—
244#399—1221no—
245#392—611no—
246#392—1221no—
247#392C2×D6111yescharacteristic
248#380—1221no—
249#376—611no—
250#342—611no—
251#342C2×D6111yescharacteristic
252#324—1221no—
253#323—611no—
254#323C2×D6111yescharacteristic
255C61#1182111yescharacteristic, complemented, Sylow
256C22×D4—21no—
257C22×D4—611no—
258C22×D4—1221no—
259C22×D4C4×D6111yescharacteristic
260C23×C4—611no—
261C23×C4—611no—
262C23×C4—1221no—
263C2×M16—2441no—
264C4×D4—2441no—
265C4×D4—2441no—
266C4×D4—2444no—
267C4×D4—2444no—
268C4×D4—2441no—
269C4×D4—2441no—
270C2×C4⋊C4—611no—
271C2×C4⋊C4—611no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—2441no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—611no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1221no—
282C2×C22⋊C4—1221no—
283C2×C22⋊C4C22×D6111yescharacteristic
284C2×C42—611no—
285C2×C42—1221no—
286#99—2442no—
287C22⋊C8—21no—
288C22⋊C8—1221no—
289C22⋊C8—2441no—
290#95—611no—
291#95—1221no—
292#95—2441no—
293#95C4×D6111yescharacteristic
294C24—21no—
295C24—611no—
296C24D4×D6111yescharacteristic
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—42no—
303C2×D4—1221no—
304C2×D4—1221no—
305C2×D4—2441no—
306C2×D4—2441no—
307C2×D4—2442no—
308C2×D4—2442no—
309C2×D4—2442no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—611no—
313C22×C4—611no—
314C22×C4—611no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—2442no—
322C22×C4—2441no—
323C22×C4—2441no—
324C22×C4—2442no—
325C22×C4—2442no—
326C22×C4—2442no—
327C22×C4—2441no—
328C22×C4C2×C4×D6111yescharacteristic
329C22×C4D4×D6111yescharacteristic
330M16—4882no—
331C2×C8—41no—
332C2×C8—2441no—
333C4⋊C4—4882no—
334C4⋊C4—2441no—
335C4⋊C4—2441no—
336C4⋊C4—2442no—
337C4⋊C4—2442no—
338C22⋊C4—41no—
339C22⋊C4—42no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—2441no—
343C22⋊C4—2442no—
344C22⋊C4—2442no—
345C22⋊C4—2442no—
346C22⋊C4—2442no—
347C22⋊C4—2441no—
348C22⋊C4—2441no—
349C42—1221no—
350C42—1221no—
351C42—1224no—
352C23—21no—
353C23—21no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—1221no—
364C23—1221no—
365C23—1221no—
366C23—2441no—
367C23—2441no—
368C23C22⋊C4×D6111yescharacteristic
369C23#1451980111yescharacteristic
370C23#1451980611yescharacteristic
371D4—42no—
372D4—44no—
373D4—44no—
374D4—42no—
375D4—2442no—
376D4—2442no—
377D4—2448no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—611no—
389C2×C4—611no—
390C2×C4—1222no—
391C2×C4—1222no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—4881no—
397C2×C4—4882no—
398C2×C4—4882no—
399C2×C4—4881no—
400C2×C4—4881no—
401C2×C4—4881no—
402C2×C4—4881no—
403C2×C4—2442no—
404C2×C4—2442no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C8—81no—
412C8—4881no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—41no—
418C22—41no—
419C22—42no—
420C22—42no—
421C22—41no—
422C22—41no—
423C22—42no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—4881no—
430C22—2442no—
431C22—2441no—
432C22—2441no—
433C22—2441no—
434C22#99×D6111yescharacteristic
435C22#1683976011yescharacteristic
436C22#1683977711yescharacteristic
437C4—42no—
438C4—41no—
439C4—41no—
440C4—161no—
441C4—612no—
442C4—1221no—
443C4—9761no—
444C4—4881no—
445C4—2442no—
446C4—2441no—
447C4—2441no—
448C2—21no—
449C2—21no—
450C2—41no—
451C2—41no—
452C2—82no—
453C2—4881no—
454C2#2144435911yescharacteristic
455C2#2144745711yescharacteristic
456C2#353×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1343C2
socleC22×C61C2×#99
prime radical#21449097C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1343D61
hypocenterC61#11821
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #21445806C2semidirect
3. #21444154C2semidirect
4. #21443844C2semidirect
5. #21443842C2semidirect
6. #21443816C2semidirect
7. C61×#1343C2semidirect
9. C2×D4×Dic61C4semidirect
14. #16839699C4semidirect
18. #16839670C4semidirect
20. #16839607C4semidirect
226. #1343D61semidirect
255. C61#11821semidirect

Maximal subgroups

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

subgroupindex
#214490972
#214458062
#214441542
#214438442
#214438422
#214438162
C61×#13432
#1182161