Finite Group Databasebeta

← #30603432

Subgroups — #30603432

Order 15616.

778 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840765C211yesmaximal, characteristic
2C2×#16840642C212yesmaximal
3C2×#16840642C212yesmaximal
4#21461482C211yesmaximal, characteristic
5C2×#16839657C211yesmaximal, characteristic
6C22×#11758217C2212yes—
7C22×#11758217C2212yes—
8#16840765—24no—
9C2×#14519844—21no—
10C2×C4⋊#92420—21no—
11#16840642—24no—
12#16840642—24no—
13#16840628—21no—
14#16840628—21no—
15C22×#11758196C411yescharacteristic
16C22×#11758196C2211yescharacteristic
17C22×#11758196C2211yescharacteristic
18C22×C4×Dic61C2211yescharacteristic
19#16839657—21no—
20#16839657—21no—
21#16839657—21no—
22#16839657—21no—
23C2×#14519684C411yescharacteristic
24C2×#14519684C411yescharacteristic
25C22×C4⋊C4×C61C411yescharacteristic
26C2×#11758217—22no—
27C2×#11758217—22no—
28C2×#11758217—22no—
29C2×#11758217—22no—
30C2×#11758217—22no—
31C2×#11758217—22no—
32C2×#11758217—22no—
33C2×#11758217—22no—
34C2×#11758217—22no—
35C2×#11758217—22no—
36C2×#11758217D414yes—
37C2×#11758217Q814yes—
38C22×#92420—22no—
39C22×#92420—22no—
40#14519844—24no—
41C4⋊#92420—24no—
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61C2×C411yescharacteristic
44C23×Dic61C2×C411yescharacteristic
45C23×Dic61C2311yescharacteristic
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758196—21no—
50C2×#11758196—21no—
51C2×#11758196—21no—
52C2×#11758196—22no—
53C2×#11758196—21no—
54C2×#11758196—21no—
55C2×#11758196—22no—
56C2×#11758196—42no—
57C2×#11758196D412yes—
58C2×#11758196Q812yes—
59C2×C4×Dic61—22no—
60C2×C4×Dic61—22no—
61C2×C4×Dic61D411yescharacteristic
62C2×C4×Dic61D411yescharacteristic
63C2×C4×Dic61D411yescharacteristic
64C2×C4×Dic61D411yescharacteristic
65#14519684—21no—
66#14519684—21no—
67#14519684—21no—
68#14519684—21no—
69C23×C4×C61C2×C411yescharacteristic
70C23×C4×C61C2×C411yescharacteristic
71C23×C4×C61C2×C411yescharacteristic
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61—42no—
75C24×C61C22×C411yescharacteristic
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61—21no—
81C22×C4×C61—22no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C22⋊C411yescharacteristic
89C22×C4×C61C4⋊C412yes—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—22no—
93C22×Dic61—22no—
94C22×Dic61—21no—
95C22×Dic61—22no—
96C22×Dic61—41no—
97C22×Dic61—41no—
98C22×Dic61—41no—
99C22×Dic61—41no—
100C22×Dic61—41no—
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C4⋊C412yes—
104C22×Dic61C2×D412yes—
105C22×Dic61C2×D411yescharacteristic
106C22×Dic61C2×D411yescharacteristic
107C22×Dic61C2×D411yescharacteristic
108C22×Dic61C2×Q812yes—
109C22×Dic61C2×Q811yescharacteristic
110C22×Dic61#4111yescharacteristic
111C22×Dic61#4111yescharacteristic
112C22×Dic61#4112yes—
113C22×Dic61#4112yes—
114#11758217—24no—
115#11758217—24no—
116#11758217—24no—
117#11758217—24no—
118#11758217—42no—
119#11758217—42no—
120#11758217—42no—
121#11758217—42no—
122C2×#92420—24no—
123C2×#92420—24no—
124C2×#92420—42no—
125C2×#92420—42no—
126C2×#92420—42no—
127C2×#92420—42no—
128C4⋊C4×C61—42no—
129C4⋊C4×C61—42no—
130#11758196—22no—
131#11758196—22no—
132#11758196—22no—
133#11758196—22no—
134#11758196—42no—
135#11758196—42no—
136#11758196—41no—
137#11758196—42no—
138#11758196—41no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C4×Dic61—22no—
142C4×Dic61—22no—
143C4×Dic61—21no—
144C4×Dic61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—21no—
149C23×C61C2×C22⋊C411yescharacteristic
150C23×C61C2×C4⋊C411yescharacteristic
151C23×C61#11711yescharacteristic
152C23×C61C4×D412yes—
153C23×C61C4×Q812yes—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—22no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—44no—
161C2×C4×C61—42no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—42no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—82no—
169C2×C4×C61#10012yes—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—22no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—44no—
177C2×Dic61—42no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—42no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—82no—
185C2×Dic61#10112yes—
186C2×Dic61#12011yescharacteristic
187C2×Dic61#12112yes—
188C2×Dic61#12111yescharacteristic
189C2×Dic61#12111yescharacteristic
190C2×Dic61#12112yes—
191C2×Dic61C22⋊Q812yes—
192C2×Dic61C22⋊Q811yescharacteristic
193C2×Dic61C22⋊Q812yes—
194C2×Dic61C22⋊Q812yes—
195C2×Dic61C22⋊Q811yescharacteristic
196C2×Dic61#12312yes—
197C2×Dic61#12311yescharacteristic
198C2×Dic61#12411yescharacteristic
199C2×Dic61#12512yes—
200C2×Dic61#12512yes—
201C2×Dic61#12612yes—
202C2×Dic61C4⋊Q812yes—
203C2×Dic61C4⋊Q811yescharacteristic
204#92420—44no—
205#92420—44no—
206#11204—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—22no—
212C22×C61—22no—
213C22×C61—22no—
214C22×C61—22no—
215C22×C61#38011yescharacteristic
216C22×C61#38611yescharacteristic
217C22×C61#38712yes—
218C22×C61#38912yes—
219C22×C61#39111yescharacteristic
220C22×C61C2×#10011yescharacteristic
221C22×C61C2×#10111yescharacteristic
222C22×C61#41311yescharacteristic
223C22×C61#41311yescharacteristic
224C4×C61—22no—
225C4×C61—42no—
226C4×C61—41no—
227C4×C61—81no—
228Dic61—22no—
229Dic61—42no—
230Dic61—41no—
231Dic61—81no—
232Dic61#39411yescharacteristic
233Dic61#39511yescharacteristic
234Dic61#39612yes—
235Dic61#39811yescharacteristic
236Dic61#39812yes—
237Dic61#40011yescharacteristic
238C2×#423—611no—
239C2×#389—611no—
240C2×#343—612no—
241C2×#343—612no—
242#1728—611no—
243C2×C61—22no—
244C2×C61—22no—
245C2×C61#144111yescharacteristic
246C2×C61#180011yescharacteristic
247C2×C61#180111yescharacteristic
248C2×C61#190011yescharacteristic
249C2×C61#190111yescharacteristic
250C2×C61#199711yescharacteristic
251C2×C61#199811yescharacteristic
252C22×M16—612no—
253C22×M16—612no—
254C22×C4⋊C4—611no—
255C22×C4⋊C4—611no—
256C22×C4⋊C4—611no—
257C22×C4⋊C4#692311yescharacteristic
258C22×C42—611no—
259#423—1224no—
260C2×C4⋊C8—1221no—
261C2×C4⋊C8—1221no—
262#389—1221no—
263#389—1221no—
264#389—1221no—
265#389—1221no—
266C2×#95—611no—
267C2×#95—611no—
268#343—1224no—
269#343—1224no—
270#336—1221no—
271#336—1221no—
272C61#1120411yescharacteristic, complemented, Sylow
273C23×C4—611no—
274C23×C4—611no—
275C23×C4—611no—
276C23×C4—611no—
277C23×C4C2×#692311yescharacteristic
278C23×C4C2×#692311yescharacteristic
279C23×C4C2×#692311yescharacteristic
280C2×M16—614no—
281C2×M16—614no—
282C2×M16—1222no—
283C2×M16—1222no—
284C2×M16—1222no—
285C2×M16—1222no—
286C2×M16—1222no—
287C2×M16—1222no—
288C2×M16—1222no—
289C2×M16—1222no—
290C2×M16—1222no—
291C2×M16—1222no—
292C22×C8—1222no—
293C22×C8—1222no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—612no—
298C2×C4⋊C4—612no—
299C2×C4⋊C4—1221no—
300C2×C4⋊C4—1221no—
301C2×C4⋊C4—1221no—
302C2×C4⋊C4—1221no—
303C2×C4⋊C4—1222no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4—1222no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—2442no—
310C2×C42—611no—
311C2×C42—611no—
312C2×C42—611no—
313C2×C42—611no—
314C2×C42—1222no—
315C2×C42—1222no—
316C4⋊C8—1224no—
317C4⋊C8—1224no—
318#95—1221no—
319#95—1221no—
320#95—1221no—
321#95—1221no—
322C24C22×#692311yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—611no—
335C22×C4—611no—
336C22×C4—611no—
337C22×C4—611no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—612no—
341C22×C4—612no—
342C22×C4—612no—
343C22×C4—612no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—612no—
347C22×C4—1222no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1221no—
353C22×C4—2441no—
354C22×C4—2441no—
355C22×C4—2441no—
356C22×C4—2441no—
357C22×C4—2441no—
358C22×C4C4⋊#692312yes—
359C22×C4C22⋊#692311yescharacteristic
360C22×C4C22⋊#692311yescharacteristic
361M16—1224no—
362M16—1224no—
363M16—1224no—
364M16—1224no—
365M16—2442no—
366M16—2442no—
367M16—2442no—
368M16—2442no—
369C2×C8—1224no—
370C2×C8—1224no—
371C2×C8—2442no—
372C2×C8—2442no—
373C2×C8—2442no—
374C2×C8—2442no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—1222no—
378C4⋊C4—1222no—
379C4⋊C4—1222no—
380C4⋊C4—1222no—
381C4⋊C4—2442no—
382C4⋊C4—2441no—
383C4⋊C4—2442no—
384C4⋊C4—2441no—
385C4⋊C4—2442no—
386C42—1221no—
387C42—1221no—
388C42—1222no—
389C42—1221no—
390C42—1222no—
391C42—1221no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23C2×C22⋊#692311yescharacteristic
397C23C2×C4⋊#692311yescharacteristic
398C23#1451985611yescharacteristic
399C23D4×#692312yes—
400C23Q8×#692312yes—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—82no—
416C2×C4—611no—
417C2×C4—611no—
418C2×C4—611no—
419C2×C4—611no—
420C2×C4—611no—
421C2×C4—612no—
422C2×C4—611no—
423C2×C4—612no—
424C2×C4—612no—
425C2×C4—612no—
426C2×C4—612no—
427C2×C4—612no—
428C2×C4—612no—
429C2×C4—612no—
430C2×C4—612no—
431C2×C4—612no—
432C2×C4—611no—
433C2×C4—611no—
434C2×C4—612no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1222no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—4882no—
442C2×C4—2444no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2442no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2442no—
450C2×C4#1451983712yes—
451C8—2444no—
452C8—2444no—
453C22—22no—
454C22—22no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—22no—
460C22—22no—
461C22#1684070411yescharacteristic
462C22#1684071011yescharacteristic
463C22#1684071112yes—
464C22#1684071312yes—
465C22(C2×#6923)⋊Q811yescharacteristic
466C22C2×#1451983711yescharacteristic
467C22D61⋊#10111yescharacteristic
468C22#1684074811yescharacteristic
469C22#1684074911yescharacteristic
470C4—22no—
471C4—41no—
472C4—42no—
473C4—81no—
474C4—611no—
475C4—611no—
476C4—612no—
477C4—611no—
478C4—612no—
479C4—611no—
480C4—1222no—
481C4—4881no—
482C4—2441no—
483C4—2442no—
484C2—22no—
485C2—22no—
486C2#2146100411yescharacteristic
487C2#2146168311yescharacteristic
488C2#2146168611yescharacteristic
489C2#2146184411yescharacteristic
490C2#2146184711yescharacteristic
491C2#2146201111yescharacteristic
492C2#2146201311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#11204
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
272. C61#11204semidirect

Maximal subgroups

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

subgroupindex
C2×#168407652
C2×#168406422
#214614822
C2×#168396572
#1120461