Finite Group Databasebeta

← #29595524

Subgroups — #29595524

Order 15616.

1070 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 1070 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16840308C211yesmaximal, characteristic
2C2×#16839560C212yesmaximal, complemented
3C2×#16839558C212yesmaximal, complemented
4#21445747C211yesmaximal, characteristic, complemented
5C61×#1785C211yesmaximal, characteristic, complemented
6C22×#11758222C411yescharacteristic
7#16840308—24no—
8#16840308—24no—
9C2×#14519775C2211yescharacteristic
10C2×#14519773C411yescharacteristic
11C2×#14519766C2211yescharacteristic
12C2×#14519764C411yescharacteristic
13C2×#14519749—21no—
14C2×#14519749—21no—
15C2×C4×C22⋊D61—21no—
16C2×C4×C22⋊D61—21no—
17C22×C4×Dic61C411yescharacteristic
18C2×#14519696C2212yes—
19C2×#14519694—21no—
20#16839726—21no—
21#16839560—24no—
22#16839558—24no—
23C22×#41×C61C2211yescharacteristic
24C2×#101×C61C2212yes—
25C2×#100×C61—21no—
26C61×#407—21no—
27C2×#11758222—22no—
28C2×#11758222—22no—
29C2×#11758222—42no—
30C2×#11758222—42no—
31C22×Dic122C2×C411yescharacteristic
32C22×D244C2×C411yescharacteristic
33C22×C22⋊D61—21no—
34C22×C22⋊D61—21no—
35C22×C22⋊D61—21no—
36C23×Dic61—21no—
37C22×C4×D61—21no—
38C2×#11758194—22no—
39#14519775—22no—
40#14519775D414yes—
41#14519773—22no—
42#14519773—22no—
43#14519766—22no—
44#14519766D414yes—
45#14519764—22no—
46#14519764—22no—
47#14519749—28no—
48#14519749—28no—
49C4×C22⋊D61—28no—
50C4×C22⋊D61—28no—
51C2×#11758196—21no—
52C2×#11758196—21no—
53C2×C22⋊Dic61—21no—
54C2×C22⋊Dic61—21no—
55C2×#11758198—21no—
56C2×#11758198—21no—
57C2×C4×Dic61—21no—
58C2×C4×Dic61—22no—
59C2×C4×Dic61—22no—
60C2×C4×Dic61C2×C411yescharacteristic
61C2×C4×Dic61C2×C411yescharacteristic
62#14519696—22no—
63#14519696—22no—
64#14519694—42no—
65C22⋊#92418—42no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—42no—
69C2×#41×C61—42no—
70C22×Q8×C61C2311yescharacteristic
71C22×D4×C61C2×C411yescharacteristic
72C22×D4×C61D411yescharacteristic
73C22×D4×C61D411yescharacteristic
74C23×C4×C61C2×C411yescharacteristic
75C23×C4×C61D411yescharacteristic
76C23×C4×C61D411yescharacteristic
77C2×M16×C61—22no—
78#101×C61—22no—
79#101×C61—22no—
80#100×C61—42no—
81C22⋊C8×C61—42no—
82C24×C61C22⋊C411yescharacteristic
83C24×C61C22⋊C411yescharacteristic
84C24×C61C22⋊C411yescharacteristic
85C23×D61—21no—
86#41×C61—48no—
87#41×C61—48no—
88C2×Q8×C61—41no—
89C2×Q8×C61—41no—
90C2×Q8×C61C2×D412yes—
91C2×Q8×C61C2×D412yes—
92C2×D4×C61—22no—
93C2×D4×C61—22no—
94C2×D4×C61—21no—
95C2×D4×C61—21no—
96C2×D4×C61—22no—
97C2×D4×C61—22no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C2×D4×C61—41no—
101C2×D4×C61—41no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—41no—
111C22×C4×C61—41no—
112C22×C4×C61C22⋊C411yescharacteristic
113C22×C4×C61C22×C411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C2×C22⋊D61—24no—
117C2×C22⋊D61—24no—
118C2×C22⋊D61—24no—
119C2×C22⋊D61—44no—
120C2×C22⋊D61—44no—
121C2×C22⋊D61—42no—
122C2×C22⋊D61—42no—
123C22×Dic61—21no—
124C22×Dic61—24no—
125C22×Dic61—21no—
126C22×Dic61—21no—
127C22×Dic61—44no—
128#11758222—48no—
129#11758222—48no—
130C2×D244—21no—
131C2×D244—41no—
132C2×D244—41no—
133C2×D244C22⋊C412yes—
134C2×C4×D61—24no—
135C2×C4×D61—42no—
136C2×C4×D61—42no—
137C2×Dic122—21no—
138C2×Dic122—41no—
139C2×Dic122—41no—
140C2×Dic122C22⋊C412yes—
141M16×C61—42no—
142M16×C61—42no—
143C2×C8×C61—42no—
144C22⋊Dic61—24no—
145C22⋊Dic61—24no—
146#11758198—24no—
147#11758198—24no—
148#11758196—24no—
149#11758196—24no—
150C4×Dic61—24no—
151C4×Dic61—21no—
152C4×Dic61—21no—
153C4×Dic61C22⋊C412yes—
154C4×Dic61C22⋊C412yes—
155#11758194—42no—
156#11758194—42no—
157C2×#92418—42no—
158C23×C61—21no—
159C23×C61—21no—
160C23×C61—21no—
161C23×C61—21no—
162C23×C61—21no—
163C23×C61—21no—
164C23×C61—21no—
165C23×C61—21no—
166C23×C61—42no—
167C23×C61—42no—
168C23×C61—42no—
169C23×C61#9912yes—
170C23×C61C2×C22⋊C411yescharacteristic
171C22×D61—22no—
172C22×D61—42no—
173C22×D61—42no—
174C22×D61—41no—
175C22×D61—41no—
176Q8×C61—42no—
177Q8×C61—42no—
178D4×C61—44no—
179D4×C61—44no—
180D4×C61—42no—
181D4×C61—42no—
182C2×C4×C61—24no—
183C2×C4×C61—24no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—21no—
191C2×C4×C61—21no—
192C2×C4×C61—44no—
193C2×C4×C61—44no—
194C2×C4×C61#9912yes—
195C2×C4×C61C2×C22⋊C411yescharacteristic
196C2×C4×C61C2×C22⋊C411yescharacteristic
197C2×C4×C61#12012yes—
198C2×C4×C61#12012yes—
199C22⋊D61—48no—
200C22⋊D61—48no—
201C22⋊D61—48no—
202C2×Dic61—24no—
203C2×Dic61—22no—
204C2×Dic61—22no—
205C2×Dic61—22no—
206C2×Dic61—48no—
207C2×Dic61—42no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210D244—42no—
211D244—42no—
212C4×D61—48no—
213Dic122—42no—
214Dic122—42no—
215C8×C61—82no—
216#92418—82no—
217#12701—611nomaximal, Sylow
218C22×C61—22no—
219C22×C61—22no—
220C22×C61—42no—
221C22×C61—42no—
222C22×C61—42no—
223C22×C61—42no—
224C22×C61—42no—
225C22×C61—42no—
226C22×C61—42no—
227C22×C61—41no—
228C22×C61—41no—
229C22×C61—81no—
230C22×C61—81no—
231C22×C61#37911yescharacteristic
232C22×C61C2×#9911yescharacteristic
233C22×C61C2×#9911yescharacteristic
234C2×D61—42no—
235C2×D61—42no—
236C2×D61—42no—
237C2×D61—82no—
238C2×D61—82no—
239C4×C61—22no—
240C4×C61—22no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—22no—
244Dic61—24no—
245Dic61—42no—
246Dic61—42no—
247C2×#532—611no—
248C2×#356—612no—
249C2×#355—612no—
250#1785—611no—
251#1785D6111yescharacteristic, complemented
252C2×C61—21no—
253C2×C61—21no—
254C2×C61—42no—
255C2×C61—81no—
256C2×C61—81no—
257C2×C61#178111yescharacteristic
258C2×C61#213212yes—
259D61—82no—
260C22×#41—611no—
261C22×#41C2×D6111yescharacteristic
262#532—1224no—
263#532—1224no—
264C2×C4⋊Q8—611no—
265C2×#127—611no—
266C2×#124—611no—
267C2×#124—611no—
268C2×#121—1221no—
269C2×#121—1221no—
270C2×C4×D4—1221no—
271C2×C4×D4—1221no—
272C22×C42—611no—
273C2×#101—612no—
274C2×#101C2×D6112yes—
275C2×#100—21no—
276C2×#100—1221no—
277#407—21no—
278#407—1221no—
279#356—1224no—
280#355—1224no—
281C61#1270111yescharacteristic, complemented, Sylow
282C2×#41—22no—
283C2×#41—22no—
284C2×#41—42no—
285C2×#41—42no—
286C2×#41—1222no—
287C2×#41—1222no—
288C2×#41—2442no—
289C2×#41—2442no—
290C22×Q8—611no—
291C22×Q8C22×D6111yescharacteristic
292C22×D4—611no—
293C22×D4—1221no—
294C22×D4—1221no—
295C22×D4—1221no—
296C22×D4C4×D6111yescharacteristic
297C22×D4D24411yescharacteristic
298C22×D4C22⋊D6111yescharacteristic
299C23×C4—1221no—
300C23×C4—1221no—
301C23×C4C4×D6111yescharacteristic
302C23×C4D24411yescharacteristic
303C23×C4C22⋊D6111yescharacteristic
304C2×M16—22no—
305C2×M16—1222no—
306C4⋊Q8—614no—
307C4⋊Q8—1222no—
308#127—1222no—
309#127—1222no—
310#124—614no—
311#124—1222no—
312#124—1222no—
313#124—1222no—
314#121—1228no—
315#121—1228no—
316C4×D4—1228no—
317C4×D4—1228no—
318C2×C4⋊C4—1221no—
319C2×C4⋊C4—1221no—
320C2×C22⋊C4—1221no—
321C2×C22⋊C4—1221no—
322C2×C22⋊C4—1221no—
323C2×C22⋊C4—1221no—
324C2×C42—611no—
325C2×C42—611no—
326C2×C42—1222no—
327C2×C42—1222no—
328C2×C42—1221no—
329#101—22no—
330#101—22no—
331#101—1222no—
332#101—1222no—
333#100—42no—
334#100—2442no—
335C22⋊C8—42no—
336C22⋊C8—2442no—
337C24—1221no—
338C24#1175819811yescharacteristic
339C24#1175819811yescharacteristic
340C24#1175819811yescharacteristic
341#41—48no—
342#41—48no—
343#41—2448no—
344#41—2448no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8—612no—
348C2×Q8—1221no—
349C2×Q8—2441no—
350C2×Q8—2441no—
351C2×Q8D4×D6112yes—
352C2×Q8D4×D6112yes—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—612no—
364C2×D4—1224no—
365C2×D4—1224no—
366C2×D4—1224no—
367C2×D4—1221no—
368C2×D4—2441no—
369C2×D4—2441no—
370C2×D4—2444no—
371C2×D4—2444no—
372C2×D4—2442no—
373C2×D4—2442no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—1224no—
385C22×C4—1221no—
386C22×C4—1224no—
387C22×C4—1221no—
388C22×C4—1221no—
389C22×C4—2442no—
390C22×C4—2444no—
391C22×C4—2442no—
392C22×C4#1175819811yescharacteristic
393C22×C4C2×C4×D6111yescharacteristic
394C22×C4C2×D24411yescharacteristic
395C22×C4C2×C22⋊D6111yescharacteristic
396M16—42no—
397M16—42no—
398M16—2442no—
399M16—2442no—
400C2×C8—42no—
401C2×C8—2442no—
402C4⋊C4—1224no—
403C4⋊C4—1224no—
404C22⋊C4—1224no—
405C22⋊C4—1224no—
406C22⋊C4—1224no—
407C22⋊C4—1224no—
408C42—612no—
409C42—612no—
410C42—1224no—
411C42—1221no—
412C42—1221no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—42no—
422C23—42no—
423C23—42no—
424C23—1222no—
425C23—2442no—
426C23—2442no—
427C23—2441no—
428C23—2441no—
429C23#1451969112yes—
430C23C2×#1175819811yescharacteristic
431Q8—42no—
432Q8—42no—
433Q8—2442no—
434Q8—2442no—
435D4—44no—
436D4—44no—
437D4—42no—
438D4—42no—
439D4—2442no—
440D4—2442no—
441D4—2448no—
442D4—2448no—
443D4—2448no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—1224no—
457C2×C4—1222no—
458C2×C4—1222no—
459C2×C4—1222no—
460C2×C4—2448no—
461C2×C4—2448no—
462C2×C4—2442no—
463C2×C4—2441no—
464C2×C4—2441no—
465C2×C4#1451969112yes—
466C2×C4C22⋊C4×D6111yescharacteristic
467C2×C4C22⋊C4×D6111yescharacteristic
468C2×C4#1451974512yes—
469C2×C4#1451974712yes—
470C8—82no—
471C8—4882no—
472C22—22no—
473C22—22no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—41no—
482C22—41no—
483C22—81no—
484C22—81no—
485C22—4882no—
486C22—4882no—
487C22—2442no—
488C22—2442no—
489C22—2442no—
490C22#1683961711yescharacteristic
491C22C2×#1451969111yescharacteristic
492C22C2×#1451969111yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—21no—
497C4—21no—
498C4—1224no—
499C4—2442no—
500C4—2442no—
501C2—21no—
502C2—21no—
503C2—42no—
504C2—81no—
505C2—81no—
506C2—4882no—
507C2#2144573311yescharacteristic
508C2#2144750212yes—
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC61×#1785C2
socleC22×C61C2×#99
prime radicalC2×#16840308C2
cosocleC22×Q8×C61C23
hypercenter#1785D61
hypocenterC61#12701
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
2. C2×#16839560C2semidirect
3. C2×#16839558C2semidirect
4. #21445747C2semidirect
5. C61×#1785C2semidirect
251. #1785D61semidirect
281. C61#12701semidirect

Maximal subgroups

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

subgroupindex
C2×#168403082
C2×#168395602
C2×#168395582
#214457472
C61×#17852
#1270161