Finite Group Databasebeta

← #29597565

Subgroups — #29597565

Order 15616.

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

normal subgroups only

This group has 694 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
1C2×#16839746C211yesmaximal, characteristic
2#21449443C211yesmaximal, characteristic
3C2×#16839560C212yesmaximal, complemented
4#21443945C212yesmaximal, complemented
5C61×#1785C211yesmaximal, characteristic
6C22×#11758194—21no—
7C2×#14519775C2211yescharacteristic
8C2×#14519764C411yescharacteristic
9C2×#14519756C411yescharacteristic
10#16839746—24no—
11C2×#14519696C2212yes—
12C2×#14519694—21no—
13#16839676—21no—
14#16839676—21no—
15#16839669C2211yescharacteristic
16#16839665C411yescharacteristic
17#16839635—21no—
18#16839635—21no—
19C4×C22⋊Dic61C411yescharacteristic
20#16839560—24no—
21C22×#41×C61C2211yescharacteristic
22C2×#101×C61C2212yes—
23C2×#100×C61—21no—
24C61×#407—21no—
25C22×Dic122C2×C411yescharacteristic
26C2×#11758194—24no—
27C2×#11758194—22no—
28C2×#11758194—42no—
29C2×#11758194—41no—
30C22×#92418—41no—
31#14519775—22no—
32#14519775—22no—
33#14519764—42no—
34#14519756—41no—
35#14519756—41no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61C2×C411yescharacteristic
48#14519696—22no—
49#14519696D414yes—
50#14519694—24no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54C2×#41×C61—22no—
55C2×#41×C61—22no—
56C2×#41×C61—41no—
57C2×#41×C61—41no—
58C2×#41×C61—42no—
59C22×Q8×C61C2311yescharacteristic
60C22×D4×C61C2×C411yescharacteristic
61C22×D4×C61D411yescharacteristic
62C22×D4×C61D411yescharacteristic
63C23×C4×C61C2×C411yescharacteristic
64C23×C4×C61D411yescharacteristic
65C23×C4×C61D411yescharacteristic
66C2×M16×C61—22no—
67#101×C61—22no—
68#101×C61—22no—
69#100×C61—42no—
70C22⋊C8×C61—41no—
71C22⋊C8×C61—41no—
72C24×C61C22⋊C411yescharacteristic
73C24×C61C22⋊C411yescharacteristic
74C24×C61C22⋊C411yescharacteristic
75#41×C61—44no—
76#41×C61—44no—
77#41×C61—44no—
78#41×C61—44no—
79C2×Q8×C61—41no—
80C2×Q8×C61—41no—
81C2×Q8×C61C2×D412yes—
82C2×Q8×C61#4112yes—
83C2×D4×C61—22no—
84C2×D4×C61—22no—
85C2×D4×C61—22no—
86C2×D4×C61—21no—
87C2×D4×C61—22no—
88C2×D4×C61—21no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C22×C4×C61—22no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—41no—
105C22×C4×C61—41no—
106C22×C4×C61C22⋊C411yescharacteristic
107C22×C4×C61C22×C411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×Dic61—21no—
111C22×Dic61—21no—
112C22×Dic61—21no—
113C22×Dic61—21no—
114C2×Dic122—22no—
115C2×Dic122—41no—
116C2×Dic122—41no—
117M16×C61—42no—
118M16×C61—42no—
119C2×C8×C61—42no—
120C22⋊Dic61—42no—
121C22⋊Dic61—42no—
122C22⋊Dic61—42no—
123C22⋊Dic61—42no—
124C22⋊Dic61—42no—
125C22⋊Dic61—42no—
126C4⋊Dic61—41no—
127#11758196—41no—
128#11758196—41no—
129#11758196—41no—
130#11758196—42no—
131#11758196—41no—
132C4×Dic61—22no—
133C4×Dic61—41no—
134#11758194—24no—
135#11758194—44no—
136#11758194—42no—
137C2×#92418—44no—
138C2×#92418—42no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61—21no—
142C23×C61—21no—
143C23×C61—21no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61#9912yes—
154C23×C61C2×C22⋊C411yescharacteristic
155Q8×C61—42no—
156Q8×C61—42no—
157D4×C61—44no—
158D4×C61—44no—
159D4×C61—42no—
160D4×C61—42no—
161C2×C4×C61—22no—
162C2×C4×C61—22no—
163C2×C4×C61—22no—
164C2×C4×C61—22no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—42no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61#9911yescharacteristic
178C2×C4×C61#9911yescharacteristic
179C2×C4×C61C4×D412yes—
180C2×C4×C61#12011yescharacteristic
181C2×C4×C61#12112yes—
182C2×C4×C61#12311yescharacteristic
183C2×Dic61—22no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195Dic122—82no—
196C8×C61—82no—
197#92418—44no—
198#13095—611nomaximal, Sylow
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—22no—
202C22×C61—42no—
203C22×C61—42no—
204C22×C61—41no—
205C22×C61—41no—
206C22×C61—41no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61#38611yescharacteristic
217C22×C61C2×#9911yescharacteristic
218C22×C61C2×#9911yescharacteristic
219C4×C61—21no—
220C4×C61—22no—
221C4×C61—22no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225Dic61—42no—
226Dic61—81no—
227Dic61—81no—
228Dic61—81no—
229C2×#413—611no—
230#2432—611no—
231C2×#356—612no—
232#1785D6111yescharacteristic
233#1394—612no—
234C2×C61—21no—
235C2×C61—21no—
236C2×C61—42no—
237C2×C61—81no—
238C2×C61—81no—
239C2×C61#189811yescharacteristic
240C2×C61#213211yescharacteristic
241C2×C61#213511yescharacteristic
242C22×#41C2×D6111yescharacteristic
243C22×M16—1221no—
244C2×C4⋊Q8—611no—
245C2×#124—611no—
246C2×C22⋊Q8—611no—
247#413—1224no—
248C2×#101—612no—
249C2×#101C2×D6112yes—
250C2×#100—21no—
251C2×#100—1221no—
252#407—21no—
253#394—1221no—
254#394—1221no—
255#391—611no—
256#390—611no—
257#385—1221no—
258#385—1221no—
259C4×C22⋊C4—611no—
260#356—1224no—
261C61#1309511yescharacteristic, complemented, Sylow
262C2×#41—22no—
263C2×#41—22no—
264C2×#41—41no—
265C2×#41—41no—
266C2×#41—42no—
267C22×Q8—611no—
268C22×Q8C22×D6111yescharacteristic
269C22×D4C4×D6111yescharacteristic
270C22×D4D24411yescharacteristic
271C22×D4C22⋊D6111yescharacteristic
272C23×C4C4×D6111yescharacteristic
273C23×C4D24411yescharacteristic
274C23×C4C22⋊D6111yescharacteristic
275C2×M16—22no—
276C2×M16—1224no—
277C2×M16—1222no—
278C2×M16—2442no—
279C2×M16—2441no—
280C22×C8—2441no—
281C4⋊Q8—1222no—
282C4⋊Q8—1222no—
283#124—2442no—
284C22⋊Q8—2441no—
285C22⋊Q8—2441no—
286C2×C4⋊C4—611no—
287C2×C4⋊C4—1221no—
288C2×C4⋊C4—1221no—
289C2×C4⋊C4—1221no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4—1221no—
292C2×C22⋊C4—1221no—
293C2×C22⋊C4—1221no—
294C2×C22⋊C4—1221no—
295C2×C22⋊C4—1221no—
296C2×C42—611no—
297C2×C42—611no—
298#101—22no—
299#101—22no—
300#101—614no—
301#101—1222no—
302#100—42no—
303#100—1224no—
304C22⋊C8—41no—
305C22⋊C8—41no—
306#95—1221no—
307#95—1221no—
308#95—1221no—
309C24#1175819811yescharacteristic
310C24#1175819811yescharacteristic
311C24#1175819811yescharacteristic
312#41—44no—
313#41—44no—
314#41—44no—
315#41—44no—
316C2×Q8—41no—
317C2×Q8—41no—
318C2×Q8—1222no—
319C2×Q8—2441no—
320C2×Q8—2441no—
321C2×Q8D4×D6112yes—
322C2×Q8#1175822412yes—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—21no—
327C2×D4—22no—
328C2×D4—21no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4#1175819811yescharacteristic
351C22×C4C2×C4×D6111yescharacteristic
352C22×C4C2×D24411yescharacteristic
353C22×C4C2×C22⋊D6111yescharacteristic
354M16—42no—
355M16—42no—
356M16—1224no—
357M16—2444no—
358M16—2442no—
359C2×C8—42no—
360C2×C8—2444no—
361C2×C8—2442no—
362C4⋊C4—2441no—
363C4⋊C4—2441no—
364C4⋊C4—2441no—
365C4⋊C4—2441no—
366C4⋊C4—2442no—
367C4⋊C4—2441no—
368C22⋊C4—2442no—
369C22⋊C4—2442no—
370C22⋊C4—2442no—
371C22⋊C4—2442no—
372C22⋊C4—2442no—
373C22⋊C4—2442no—
374C42—1222no—
375C42—2441no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23#1451969112yes—
391C23C2×#1175819811yescharacteristic
392Q8—42no—
393Q8—42no—
394Q8—4882no—
395D4—44no—
396D4—44no—
397D4—42no—
398D4—42no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—1222no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4#1451969111yescharacteristic
428C2×C4#1451969111yescharacteristic
429C2×C4#1451973712yes—
430C2×C4#1451974711yescharacteristic
431C2×C4#1451974912yes—
432C2×C4#1451976111yescharacteristic
433C8—82no—
434C8—2444no—
435C22—21no—
436C22—21no—
437C22—22no—
438C22—42no—
439C22—42no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22#1683963911yescharacteristic
453C22C2×#1451969111yescharacteristic
454C22C2×#1451969111yescharacteristic
455C4—22no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—22no—
461C4—4881no—
462C4—4881no—
463C4—4881no—
464C4—2442no—
465C2—21no—
466C2—21no—
467C2—42no—
468C2—81no—
469C2—81no—
470C2#2144627011yescharacteristic
471C2#2144750211yescharacteristic
472C2#2144751311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC61×#1785C2
socleC22×C61C2×#99
prime radicalC22×#41×C61C22
cosocleC22×Q8×C61C23
hypercenter#1785D61
hypocenterC61#13095
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #1785

Complements

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

NH ≅ G/Ntype
3. C2×#16839560C2semidirect
4. #21443945C2semidirect
261. C61#13095semidirect

Maximal subgroups

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

subgroupindex
C2×#168397462
#214494432
C2×#168395602
#214439452
C61×#17852
#1309561