Finite Group Databasebeta

← #30600679

Subgroups — #30600679

Order 15616.

552 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 90 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#21462327C211yesmaximal, characteristic
2#21462008C211yesmaximal, characteristic
3#21461722C211yesmaximal, characteristic
4#21461259C211yesmaximal, characteristic
5#21460682C211yesmaximal, characteristic
6#21460661C211yesmaximal, characteristic
7C2×#16840091C211yesmaximal, characteristic
8C2×#14519856—21no—
9D61⋊(C22⋊C8)C2211yescharacteristic
10#16840713—21no—
11#16840711—22no—
12#16840705—21no—
13#16840704C2211yescharacteristic
14#16840704C2211yescharacteristic
15C4⋊C4×#6923—21no—
16C4×C22⋊#6923C2211yescharacteristic
17#16840640—21no—
18#16840640—21no—
19#16840635—21no—
20#16840635—21no—
21#16840616—22no—
22C2×#14519753C2211yescharacteristic
23C2×C4⋊C4×D61C2211yescharacteristic
24#16840091—21no—
25#16840091—21no—
26#16840091—21no—
27#16840091—21no—
28C2×#14519709C411yescharacteristic, complemented
29C2×#14519708C411yescharacteristic, complemented
30C2×#14519701C411yescharacteristic, complemented
31C2×#14519689C2211yescharacteristic
32C2×#103×C61C411yescharacteristic, complemented
33C2×D61⋊C8—21no—
34#14519856—42no—
35#14519856—42no—
36C2×C4⋊#6923—22no—
37C2×C4⋊#6923—21no—
38C2×C4⋊#6923—21no—
39C2×C22⋊#6923—21no—
40C2×C22⋊#6923—21no—
41C2×C22⋊#6923D411yescharacteristic
42C2×C22⋊#6923D411yescharacteristic
43C2×C4×#6923—22no—
44C2×C4×#6923—21no—
45#14519834—21no—
46C22⋊#92420—21no—
47(C2×#6923)⋊C4—22no—
48(C2×#6923)⋊C4—22no—
49(C2×#6923)⋊C4—21no—
50(C2×#6923)⋊C4—21no—
51(C2×#6923)⋊C4D412yes—
52C22×C4×D61—21no—
53C22×C4×D61C2311yescharacteristic
54C22×#92418C2×C411yescharacteristic
55#14519753—21no—
56#14519753—21no—
57#14519753—21no—
58#14519753—21no—
59C2×C4⋊Dic61C2×C411yescharacteristic
60C2×C4⋊Dic61C2×C411yescharacteristic
61C2×#11758196—21no—
62C2×#11758196—21no—
63C4⋊C4×D61—21no—
64C4⋊C4×D61—21no—
65C4⋊C4×D61D411yescharacteristic
66C4⋊C4×D61D411yescharacteristic
67C4⋊C4×D61D411yescharacteristic
68C4⋊C4×D61D411yescharacteristic
69C2×#11758198—21no—
70#14519709—21no—
71#14519709—21no—
72#14519708—21no—
73#14519708—21no—
74#14519701—21no—
75#14519701—21no—
76#14519689—21no—
77#14519689—21no—
78C22×Q8×C61C2×C411yescharacteristic
79C22×C8×C61C2×C411yescharacteristic
80C2×C4⋊C4×C61C2×C411yescharacteristic
81#103×C61—21no—
82#103×C61—21no—
83C23×D61C2×D411yescharacteristic
84C22×#6923—21no—
85C22×#6923—21no—
86C22×#6923—22no—
87C22×#6923—41no—
88C2×Q8×C61—21no—
89C2×Q8×C61—21no—
90C2×Q8×C61—41no—
91C2×Q8×C61—41no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61C22×C411yescharacteristic
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61#4111yescharacteristic
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C4×D61—41no—
107C2×C4×D61—41no—
108C2×C4×D61C2×D411yescharacteristic
109C2×C4×D61C2×D411yescharacteristic
110C2×C4×D61C2×D411yescharacteristic
111C2×C4×D61#4111yescharacteristic
112C22⋊#6923—21no—
113C22⋊#6923—21no—
114C22⋊#6923—21no—
115C22⋊#6923—41no—
116C22⋊#6923—41no—
117C22⋊#6923—41no—
118C22⋊#6923—41no—
119C22⋊#6923SD1612yes—
120C2×#92420—41no—
121C4⋊#6923—41no—
122C4⋊#6923—41no—
123C4⋊#6923—41no—
124C4⋊#6923—41no—
125C4⋊#6923—44no—
126C4×#6923—41no—
127C4×#6923—41no—
128C4×#6923—44no—
129D61⋊C8—41no—
130D61⋊C8—41no—
131C2×C8×C61—21no—
132C2×C8×C61—41no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61C22⋊C411yescharacteristic
135C4⋊C4×C61C22⋊C411yescharacteristic
136#11758198—41no—
137#11758198—41no—
138C4⋊Dic61—21no—
139C4⋊Dic61—21no—
140C4⋊Dic61—21no—
141C4⋊Dic61C22⋊C411yescharacteristic
142C4⋊Dic61C22⋊C411yescharacteristic
143#11758196—21no—
144#11758196—21no—
145#11758196—21no—
146#11758196—21no—
147#11758196—41no—
148#11758196—41no—
149C2×#92418—21no—
150C2×#92418—41no—
151C23×C61C4×D411yescharacteristic
152C22×D61—41no—
153C22×D61—41no—
154C22×D61#12011yescharacteristic
155C22×D61#12111yescharacteristic
156C22×D61C2×SD1611yescharacteristic
157C22×D61#13511yescharacteristic
158C22×D61AGL(1,ℤ/8)11yescharacteristic
159C22×D61#13711yescharacteristic
160C2×#6923—22no—
161C2×#6923—41no—
162C2×#6923—41no—
163C2×#6923—41no—
164C2×#6923—42no—
165C2×#6923—41no—
166C2×#6923—42no—
167C2×#6923—42no—
168C2×#6923—41no—
169C2×#6923—81no—
170C2×#6923—81no—
171C2×#6923—81no—
172Q8×C61—41no—
173Q8×C61—41no—
174Q8×C61—81no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—81no—
183C2×C4×C61C2×C22⋊C411yescharacteristic
184C2×C4×C61C4×D411yescharacteristic
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—81no—
192C2×Dic61#12111yescharacteristic
193C2×Dic61#12311yescharacteristic
194C4×D61—21no—
195C4×D61—21no—
196C4×D61—21no—
197C4×D61—21no—
198C4×D61—41no—
199C4×D61—41no—
200C4×D61—41no—
201C4×D61—41no—
202C4×D61—41no—
203C4×D61—41no—
204C4×D61—41no—
205C4×D61—41no—
206C4×D61—41no—
207C4×D61—41no—
208#92420—81no—
209C8×C61—41no—
210#92418—41no—
211#9256—611nomaximal, Sylow
212C22×C61—21no—
213C22×C61—21no—
214C22×C61#38611yescharacteristic
215C22×C61C4×SD1611yescharacteristic
216C22×C61#44011yescharacteristic
217C2×D61—21no—
218C2×D61—21no—
219C2×D61—21no—
220C2×D61—21no—
221C2×D61—41no—
222C2×D61—41no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61#45011yescharacteristic
226C2×D61#45211yescharacteristic
227C2×D61#46111yescharacteristic
228C2×D61#46311yescharacteristic
229#6923—42no—
230#6923—82no—
231#6923—81no—
232#6923—161no—
233C4×C61—21no—
234C4×C61—41no—
235C4×C61—41no—
236C4×C61—81no—
237C4×C61#41011yescharacteristic
238C4×C61#41011yescharacteristic
239Dic61—21no—
240Dic61—21no—
241Dic61—41no—
242Dic61—41no—
243Dic61—81no—
244C2×#483—611no—
245#2344—611no—
246#1996—611no—
247#1823—611no—
248#1520—611no—
249#1289—611no—
250#1282—611no—
251C2×C61—21no—
252C2×C61—21no—
253C2×C61#187711yescharacteristic
254C2×C61#189911yescharacteristic
255C2×C61#190511yescharacteristic
256D61—21no—
257D61—21no—
258D61—21no—
259D61—21no—
260C2×C22⋊Q8—611no—
261C2×#117—1221no—
262C22×C4⋊C4—611no—
263#483—1221no—
264#483—1221no—
265#483—1221no—
266#483—1221no—
267C2×#106—611no—
268C2×#106—611no—
269C2×#103—611no—
270C2×#103#692311yescharacteristic, complemented
271C2×C22⋊C8—611no—
272C2×C22⋊C8—611no—
273#389—1221no—
274#387—1222no—
275#381—1221no—
276#380—611no—
277#380—611no—
278C4×C4⋊C4—1221no—
279C4×C22⋊C4—611no—
280#342—1221no—
281#342—1221no—
282#340—1221no—
283#340—1221no—
284#328—1222no—
285C61#925611yescharacteristic, complemented, Sylow
286C22×Q8C2×#692311yescharacteristic
287C23×C4—611no—
288C23×C4—1221no—
289C22×C8—611no—
290C22×C8—1221no—
291C22×C8C2×#692311yescharacteristic
292C22⋊Q8—1221no—
293C22⋊Q8—1221no—
294C22⋊Q8—1221no—
295C22⋊Q8—1221no—
296#117—2442no—
297#117—2442no—
298C2×C4⋊C4—611no—
299C2×C4⋊C4—611no—
300C2×C4⋊C4—611no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4—611no—
303C2×C4⋊C4—611no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1222no—
311C2×C4⋊C4C2×#692311yescharacteristic
312C2×C22⋊C4—611no—
313C2×C22⋊C4—611no—
314C2×C22⋊C4—1221no—
315C2×C22⋊C4—1221no—
316C2×C22⋊C4—1221no—
317C2×C42—1221no—
318C2×C42—1222no—
319#106—1221no—
320#106—1221no—
321#106—1221no—
322#106—1221no—
323#103—21no—
324#103—21no—
325#103—1221no—
326#103—1221no—
327C22⋊C8—1221no—
328C22⋊C8—1221no—
329C22⋊C8—1221no—
330C22⋊C8—1221no—
331#95—612no—
332#95—1221no—
333#95—1221no—
334#95—1222no—
335#95—1222no—
336C24—611no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—41no—
340C2×Q8—41no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4—1221no—
355C22×C4—1222no—
356C22×C4—1221no—
357C22×C4—2441no—
358C22×C4—2441no—
359C22×C4—2441no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4—2441no—
363C22×C4—2441no—
364C22×C4C22×#692311yescharacteristic
365C2×C8—21no—
366C2×C8—41no—
367C2×C8—1221no—
368C2×C8—2441no—
369C2×C8—2441no—
370C2×C8—2441no—
371C2×C8—2441no—
372C4⋊C4—21no—
373C4⋊C4—611no—
374C4⋊C4—611no—
375C4⋊C4—1221no—
376C4⋊C4—1221no—
377C4⋊C4—1221no—
378C4⋊C4—1221no—
379C4⋊C4—1221no—
380C4⋊C4—1221no—
381C4⋊C4—1221no—
382C4⋊C4—2441no—
383C4⋊C4—2441no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4—2444no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C4⋊C4C22⋊#692311yescharacteristic
390C4⋊C4C22⋊#692311yescharacteristic
391C22⋊C4—612no—
392C22⋊C4—1221no—
393C22⋊C4—1221no—
394C22⋊C4—1221no—
395C22⋊C4—2441no—
396C22⋊C4—2441no—
397C22⋊C4—2441no—
398C22⋊C4—2441no—
399C22⋊C4—2441no—
400C22⋊C4—2441no—
401C42—2444no—
402C42—2441no—
403C42—2441no—
404C23—611no—
405C23—611no—
406C23—611no—
407C23—611no—
408C23—611no—
409C23—611no—
410C23—2441no—
411C23—2441no—
412C23D4×#692311yescharacteristic
413Q8—41no—
414Q8—41no—
415Q8—81no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—81no—
424C2×C4—611no—
425C2×C4—611no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—1222no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—4881no—
434C2×C4—4881no—
435C2×C4—4881no—
436C2×C4—4881no—
437C2×C4—2441no—
438C2×C4—2441no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2442no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4—2442no—
452C2×C4—2442no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4—2441no—
458C2×C4—2441no—
459C2×C4C2×C22⋊#692311yescharacteristic
460C2×C4D4×#692311yescharacteristic
461C8—41no—
462C8—4881no—
463C8—2441no—
464C22—21no—
465C22—21no—
466C22—611no—
467C22—611no—
468C22—611no—
469C22—611no—
470C22—1221no—
471C22—1221no—
472C22—1221no—
473C22—1221no—
474C22—2441no—
475C22—2441no—
476C22—2441no—
477C22—2441no—
478C22#1684071011yescharacteristic
479C22SD16×#692311yescharacteristic
480C22#1684080111yescharacteristic
481C4—21no—
482C4—41no—
483C4—41no—
484C4—81no—
485C4—1221no—
486C4—1221no—
487C4—9761no—
488C4—4882no—
489C4—4881no—
490C4—4881no—
491C4—2442no—
492C4—2441no—
493C4—2441no—
494C4#1684074111yescharacteristic
495C4#1684074211yescharacteristic
496C2—21no—
497C2—21no—
498C2—1221no—
499C2—1221no—
500C2—1221no—
501C2—1221no—
502C2#2146181211yescharacteristic
503C2#2146184211yescharacteristic
504C2#2146185411yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#103×C61C4
socleC22×C61#386
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenterC2×#103#6923
hypocenterC61#9256
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
28. C2×#14519709C4semidirect
29. C2×#14519708C4semidirect
30. C2×#14519701C4semidirect
32. C2×#103×C61C4semidirect
270. C2×#103#6923semidirect
285. C61#9256semidirect

Maximal subgroups

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

subgroupindex
#214623272
#214620082
#214617222
#214612592
#214606822
#214606612
C2×#168400912
#925661