Finite Group Databasebeta

← #29580363

Subgroups — #29580363

Order 15616.

568 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 85 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#21456625C211yesmaximal, characteristic
2#21455767C211yesmaximal, characteristic, complemented
3#21446803C211yesmaximal, characteristic, complemented
4#21445918C211yesmaximal, characteristic, complemented
5#21444335C211yesmaximal, characteristic
6#21443725C211yesmaximal, characteristic, complemented
7C61×#2624C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9#16840103—22no—
10#16840097—21no—
11#16840097—21no—
12#16840092—21no—
13#16840073—21no—
14#16840006—22no—
15#16839913—21no—
16#16839900—21no—
17#16839805—21no—
18#16839770—21no—
19#16839726C2211yescharacteristic
20#16839726C2211yescharacteristic
21C4×C22⋊Dic61C2211yescharacteristic
22#16839528—22no—
23#16839521—22no—
24#16839496—22no—
25C2×#121×C61C2211yescharacteristic
26C2×#117×C61C2211yescharacteristic
27C61×#399—21no—
28C61×#397—21no—
29C61×#394—22no—
30C61×#390—21no—
31C61×#389—21no—
32C61×#380C2211yescharacteristic
33C22×Dic122D411yescharacteristic
34C2×#11758200—22no—
35C2×#11758194—21no—
36C2×#11758194D412yes—
37#14519756—21no—
38#14519756—21no—
39#14519756—21no—
40#14519756—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C4×Dic61—21no—
46#14519710—22no—
47#14519710—22no—
48#14519708—22no—
49#14519700—22no—
50#14519700—22no—
51#14519700—22no—
52#14519698—22no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56C22⋊#92418D412yes—
57#14519684—21no—
58C22×D4×C61—21no—
59C22×D4×C61D411yescharacteristic
60C23×C4×C61C2311yescharacteristic
61#121×C61—21no—
62#121×C61—21no—
63#121×C61—21no—
64#121×C61—21no—
65#117×C61—21no—
66#117×C61—21no—
67#117×C61—21no—
68#117×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—22no—
71C2×C4⋊C4×C61D411yescharacteristic
72C2×C4⋊C4×C61D411yescharacteristic
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61—22no—
77C2×C22⋊C4×C61—22no—
78C2×C22⋊C4×C61D412yes—
79C2×C42×C61—21no—
80#95×C61—22no—
81#95×C61—21no—
82C24×C61—21no—
83C24×C61C2×D411yescharacteristic
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—42no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—82no—
90C22×C4×C61—21no—
91C22×C4×C61—22no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—42no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61#4111yescharacteristic
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—41no—
104C2×Dic122—21no—
105C2×Dic122—21no—
106C2×Dic122—42no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—42no—
114C4⋊C4×C61—82no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C22⋊C4×C61—42no—
120C22⋊C4×C61—82no—
121C22⋊C4×C61—82no—
122C42×C61—41no—
123C42×C61—41no—
124C22⋊Dic61—22no—
125C22⋊Dic61—41no—
126C22⋊Dic61—41no—
127C22⋊Dic61—41no—
128#11758200—82no—
129C4⋊Dic61—21no—
130C4⋊Dic61—21no—
131#11758196—41no—
132#11758196—41no—
133C4×Dic61—42no—
134#11758194—42no—
135#11758194—42no—
136C2×#92418—22no—
137C2×#92418—22no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—42no—
143C23×C61—42no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61#12011yescharacteristic
148C23×C61#12111yescharacteristic
149C23×C61#12711yescharacteristic
150D4×C61—42no—
151D4×C61—81no—
152D4×C61—82no—
153D4×C61—82no—
154C2×C4×C61—22no—
155C2×C4×C61—22no—
156C2×C4×C61—22no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61—41no—
164C2×C4×C61—42no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—42no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×Dic61—42no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—81no—
179C2×Dic61—81no—
180C2×Dic61—81no—
181C2×Dic61—81no—
182Dic122—42no—
183Dic122—42no—
184#92418—42no—
185#92418—42no—
186#9936—611nomaximal, Sylow
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61—82no—
198C22×C61—82no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61#39211yescharacteristic
203C22×C61#45511yescharacteristic
204C22×C61#45611yescharacteristic
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—82no—
209C4×C61—81no—
210C4×C61—81no—
211C4×C61—81no—
212C4×C61#45812yes—
213Dic61—82no—
214Dic61—81no—
215Dic61—81no—
216#3193—611no—
217#3095—611no—
218#2624D6111yescharacteristic
219#1996—611no—
220#1826—611no—
221#1507—611no—
222#1305—611no—
223C2×C61—21no—
224C2×C61—21no—
225C2×C61—41no—
226C2×C61—41no—
227C2×C61—161no—
228C2×C61#200711yescharacteristic
229C2×C61#200811yescharacteristic
230C2×C61#202211yescharacteristic
231C2×C22⋊Q8—611no—
232C2×#121C2×D6111yescharacteristic
233C2×#117C2×D6111yescharacteristic
234#485—1222no—
235#484—1221no—
236#484—1221no—
237#483—1221no—
238#480—1221no—
239#468—1222no—
240#450—1221no—
241#448—1221no—
242#428—1221no—
243#419—1221no—
244#407—611no—
245#407—611no—
246#399—21no—
247#397—21no—
248#394—22no—
249#390—21no—
250#389—21no—
251#380C2×D6111yescharacteristic
252C4×C22⋊C4—611no—
253#342—1222no—
254#339—1222no—
255#327—1222no—
256C61#993611yescharacteristic, complemented, Sylow
257C22×Q8—611no—
258C22×D4—21no—
259C22×D4C22⋊D6111yescharacteristic
260C23×C4C22×D6111yescharacteristic
261C2×SD16—1222no—
262C2×M16—612no—
263C2×M16—1221no—
264C22⋊Q8—1221no—
265C22⋊Q8—1221no—
266C22⋊Q8—1221no—
267C22⋊Q8—1221no—
268#121—21no—
269#121—21no—
270#121—21no—
271#121—21no—
272#117—21no—
273#117—21no—
274#117—21no—
275#117—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4C22⋊D6111yescharacteristic
281C2×C4⋊C4C22⋊D6111yescharacteristic
282C2×C4⋊C4C22⋊D6111yescharacteristic
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1221no—
289C2×C22⋊C4C22⋊D6112yes—
290C2×C42—21no—
291C2×C42—1221no—
292#107—1222no—
293#107—1222no—
294#106—1222no—
295#103—1222no—
296#103—1222no—
297#103—1222no—
298#102—1222no—
299C22⋊C8—612no—
300C22⋊C8—1221no—
301C22⋊C8—1221no—
302C22⋊C8—1221no—
303#95—22no—
304#95—21no—
305#95—1221no—
306C24—21no—
307C24C2×C22⋊D6111yescharacteristic
308C2×Q8—1221no—
309C2×Q8—1221no—
310C2×Q8—2442no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—42no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—82no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—42no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—2441no—
325C22×C4D4×D6111yescharacteristic
326C22×C4D4×D6111yescharacteristic
327C22×C4D4×D6111yescharacteristic
328C22×C4#1175822411yescharacteristic
329C22×C4C2×C22⋊D6111yescharacteristic
330C22×C4C2×C22⋊D6111yescharacteristic
331SD16—4882no—
332M16—2442no—
333M16—2442no—
334C2×C8—1222no—
335C2×C8—1222no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—42no—
343C4⋊C4—82no—
344C4⋊C4—1221no—
345C4⋊C4—1221no—
346C4⋊C4—2441no—
347C4⋊C4—2441no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—42no—
353C22⋊C4—82no—
354C22⋊C4—82no—
355C22⋊C4—1222no—
356C22⋊C4—2441no—
357C22⋊C4—2441no—
358C22⋊C4—2441no—
359C42—41no—
360C42—41no—
361C42—2442no—
362C23—21no—
363C23—21no—
364C23—41no—
365C23—41no—
366C23—42no—
367C23—42no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23#1451974611yescharacteristic
372C23#1451974811yescharacteristic
373C23#1451977311yescharacteristic
374Q8—2442no—
375Q8—2442no—
376D4—42no—
377D4—81no—
378D4—82no—
379D4—82no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—4881no—
398C2×C4—4881no—
399C2×C4—4881no—
400C2×C4—4881no—
401C2×C4—2442no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4#1451974511yescharacteristic
405C2×C4#1451974511yescharacteristic
406C2×C4#1451974911yescharacteristic
407C2×C4#1451974911yescharacteristic
408C8—2442no—
409C8—2442no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—81no—
419C22—81no—
420C22—82no—
421C22—82no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22#1683967011yescharacteristic
426C22#1683994011yescharacteristic
427C22#1683994511yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—82no—
432C4—81no—
433C4—81no—
434C4—81no—
435C4—4882no—
436C4—4881no—
437C4—4881no—
438C4#1683995112yes—
439C2—21no—
440C2—21no—
441C2—41no—
442C2—41no—
443C2—161no—
444C2#2144686611yescharacteristic
445C2#2144687211yescharacteristic
446C2#2144694711yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2624C2
socleC22×C61#392
prime radicalC2×#121×C61C22
hypercenter#2624D61
hypocenterC61#9936
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2624

Complements

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

NH ≅ G/Ntype
2. #21455767C2semidirect
3. #21446803C2semidirect
4. #21445918C2semidirect
6. #21443725C2semidirect
256. C61#9936semidirect

Maximal subgroups

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

subgroupindex
#214566252
#214557672
#214468032
#214459182
#214443352
#214437252
C61×#26242
#993661