Finite Group Databasebeta

← #30602628

Subgroups — #30602628

Order 15616.

802 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×#6923C211yesmaximal, characteristic
2#21461522C211yesmaximal, characteristic
3C2×#16840641C212yesmaximal
4#21461481C212yesmaximal
5#343×D61C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C22×C4⋊#6923C2211yescharacteristic
8C22×C4×#6923C412yes—
9C22×C4×#6923C2211yescharacteristic
10C4⋊C4×#6923—22no—
11C4⋊C4×#6923—22no—
12C2×(C2×#6923)⋊C4C412yes—
13#16840642C414yescomplemented
14#16840641—24no—
15(C2×#6923)⋊C8—22no—
16(C2×#6923)⋊C8—22no—
17C2×M16×D61C2212yes—
18C2×C4⋊C4×D61C2211yescharacteristic
19#16839531C411yescharacteristic, complemented
20#16839530C412yescomplemented
21C61×#343C411yescharacteristic, complemented
22C23×#6923C2×C411yescharacteristic
23C23×#6923C2×C411yescharacteristic
24C23×#6923C2×C412yes—
25C2×#11758213—22no—
26D61⋊M16—22no—
27D61⋊M16—22no—
28D61⋊M16—22no—
29D61⋊M16—22no—
30C2×#11758217C2×C414yes—
31C2×D61⋊C8—22no—
32C2×C4⋊#6923—22no—
33C2×C4⋊#6923—22no—
34C2×C4⋊#6923D412yes—
35C2×C4⋊#6923Q812yes—
36C2×C4×#6923—22no—
37C2×C4×#6923—21no—
38C2×C4×#6923—21no—
39C2×C4×#6923—22no—
40C2×C4×#6923—22no—
41C2×C4×#6923—44no—
42C2×C4×#6923D412yes—
43C2×C4×#6923D412yes—
44(C2×#6923)⋊C4—24no—
45C22×C4×D61C2×C412yes—
46C22×C4×D61C2311yescharacteristic
47C2×#11758194C2×C412yes—
48C2×#11758189—22no—
49M16×D61—22no—
50M16×D61—22no—
51M16×D61—22no—
52M16×D61—22no—
53C2×C8×D61—22no—
54C2×C4⋊Dic61C2×C411yescharacteristic
55C2×#11758196C2×C412yes—
56C4⋊C4×D61—22no—
57C4⋊C4×D61—22no—
58C2×M16×C61C2×C412yes—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C23×D61C22×C411yescharacteristic
61C22×#6923—21no—
62C22×#6923—21no—
63C22×#6923—22no—
64C22×#6923—22no—
65C22×#6923—22no—
66C22×#6923—21no—
67C22×#6923—21no—
68C22×#6923—22no—
69C22×#6923—41no—
70C22×#6923—41no—
71C22×#6923—42no—
72C22×#6923—42no—
73C22×#6923C22⋊C412yes—
74C22×#6923C22⋊C411yescharacteristic
75C22×#6923C22⋊C411yescharacteristic
76C22×#6923C4⋊C414yes—
77C22×C4×C61C4212yes—
78C22×C4×C61C22×C411yescharacteristic
79C22×Dic61C4212yes—
80C22×Dic61C22×C411yescharacteristic
81C2×C4×D61—22no—
82C2×C4×D61—22no—
83C2×C4×D61—42no—
84C2×C4×D61—42no—
85C2×C4×D61C2×D411yescharacteristic
86C2×C4×D61C2×D412yes—
87C2×C4×D61C2×Q811yescharacteristic
88C2×C4×D61#4112yes—
89C2×C4×D61#4112yes—
90C2×C4×D61#4111yescharacteristic
91C2×C4×D61#4111yescharacteristic
92C2×C4×D61#4112yes—
93#11758217—24no—
94#11758217—24no—
95C2×#92420—24no—
96C4⋊#6923—24no—
97C4⋊#6923—24no—
98C4×#6923—22no—
99C4×#6923—22no—
100C4×#6923—22no—
101C4×#6923—22no—
102C4×#6923—44no—
103C4×#6923—44no—
104#11758213—42no—
105#11758213—42no—
106D61⋊C8—42no—
107D61⋊C8—42no—
108M16×C61—22no—
109M16×C61—22no—
110C2×C8×C61—22no—
111C4⋊C4×C61—22no—
112C4⋊Dic61—22no—
113#11758196—24no—
114#11758194—22no—
115#11758194—22no—
116C2×#92418—22no—
117#11758189—42no—
118#11758189—42no—
119C8×D61—42no—
120C8×D61—42no—
121C23×C61C2×C4211yescharacteristic
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61C2×C22⋊C411yescharacteristic
127C22×D61C2×C4⋊C411yescharacteristic
128C22×D61#11711yescharacteristic
129C22×D61#11711yescharacteristic
130C22×D61#11711yescharacteristic
131C22×D61#11711yescharacteristic
132C2×#6923—24no—
133C2×#6923—24no—
134C2×#6923—21no—
135C2×#6923—21no—
136C2×#6923—21no—
137C2×#6923—21no—
138C2×#6923—24no—
139C2×#6923—22no—
140C2×#6923—22no—
141C2×#6923—22no—
142C2×#6923—44no—
143C2×#6923—42no—
144C2×#6923—42no—
145C2×#6923—42no—
146C2×#6923—42no—
147C2×#6923—44no—
148C2×#6923#10012yes—
149C2×#6923#10112yes—
150C2×C4×C61—22no—
151C2×C4×C61—42no—
152C2×C4×C61#11712yes—
153C2×C4×C61C4×D412yes—
154C2×C4×C61C4×D411yescharacteristic
155C2×C4×C61C4×Q811yescharacteristic
156C2×Dic61—22no—
157C2×Dic61—42no—
158C2×Dic61#11712yes—
159C2×Dic61C4×D412yes—
160C2×Dic61C4×D411yescharacteristic
161C2×Dic61C4×Q811yescharacteristic
162C4×D61—44no—
163C4×D61—42no—
164C4×D61—42no—
165C4×D61#12112yes—
166C4×D61C22⋊Q812yes—
167C4×D61#12312yes—
168C4×D61#12312yes—
169C4×D61#12412yes—
170C4×D61#12512yes—
171C4×D61#12612yes—
172C4×D61#12612yes—
173#92420—44no—
174C8×C61—42no—
175#92418—42no—
176#10802—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61#37611yescharacteristic
180C22×C61C4×C22⋊C411yescharacteristic
181C22×C61C4×C4⋊C411yescharacteristic
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—21no—
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—21no—
188C2×D61—21no—
189C2×D61—21no—
190C2×D61—21no—
191C2×D61—21no—
192C2×D61#38011yescharacteristic
193C2×D61#38111yescharacteristic
194C2×D61#38211yescharacteristic
195C2×D61#38311yescharacteristic
196C2×D61C2×#10011yescharacteristic
197C2×D61C2×#10111yescharacteristic
198C2×D61#41311yescharacteristic
199C2×D61#41311yescharacteristic
200#6923—22no—
201#6923—22no—
202#6923—44no—
203#6923—42no—
204C4×C61—42no—
205C4×C61#38712yes—
206C4×C61#38812yes—
207Dic61—42no—
208Dic61#38712yes—
209Dic61#38812yes—
210C2×C4×C4⋊C4—611no—
211C2×#343—611no—
212C2×#343—611no—
213C2×#343—612no—
214#1728—612no—
215C2×C61—21no—
216C2×C61—21no—
217C2×C61#143411yescharacteristic
218C2×C61C4×#10011yescharacteristic
219C2×C61C4×#10111yescharacteristic
220D61—21no—
221D61—21no—
222D61#180011yescharacteristic
223D61#180111yescharacteristic
224D61#182111yescharacteristic
225D61#182211yescharacteristic
226C22×M16—612no—
227C22×M16—612no—
228C22×C4⋊C4—611no—
229C22×C4⋊C4—611no—
230C22×C42—611no—
231C22×C42—612no—
232C4×C4⋊C4—1222no—
233C4×C4⋊C4—1222no—
234C2×#95—612no—
235#343—614no—
236#343—612no—
237#343—611no—
238#343—1224no—
239#343#692311yescharacteristic, complemented
240#336—1222no—
241#336—1222no—
242C61#1080211yescharacteristic, complemented, Sylow
243C23×C4—611no—
244C23×C4—611no—
245C23×C4—612no—
246C23×C4—611no—
247C23×C4—612no—
248C2×M16—614no—
249C2×M16—612no—
250C2×M16—1222no—
251C2×M16—1222no—
252C2×M16—1222no—
253C2×M16—1222no—
254C2×M16—1222no—
255C2×M16—1222no—
256C2×M16—1222no—
257C2×M16—1222no—
258C2×M16—1222no—
259C2×M16—1222no—
260C2×M16C2×#692312yes—
261C22×C8—1222no—
262C22×C8—1222no—
263C2×C4⋊C4—612no—
264C2×C4⋊C4—612no—
265C2×C4⋊C4—612no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—1222no—
268C2×C4⋊C4—1222no—
269C2×C4⋊C4—1222no—
270C2×C4⋊C4—1222no—
271C2×C4⋊C4C2×#692311yescharacteristic
272C2×C42—612no—
273C2×C42—612no—
274C2×C42—1222no—
275C2×C42—1221no—
276C2×C42—1221no—
277C2×C42—1222no—
278C2×C42—1222no—
279C2×C42—2444no—
280#95—1224no—
281C24—611no—
282C22×C4—611no—
283C22×C4—612no—
284C22×C4—612no—
285C22×C4—612no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—612no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—612no—
294C22×C4—614no—
295C22×C4—612no—
296C22×C4—1222no—
297C22×C4—1222no—
298C22×C4—1222no—
299C22×C4—1222no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1222no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1222no—
306C22×C4—2442no—
307C22×C4—2442no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4—2442no—
311C22×C4—2442no—
312C22×C4C4×#692312yes—
313C22×C4C22×#692311yescharacteristic
314M16—22no—
315M16—22no—
316M16—1224no—
317M16—1224no—
318M16—1222no—
319M16—1222no—
320M16—2442no—
321M16—2442no—
322M16—2442no—
323M16—2442no—
324C2×C8—22no—
325C2×C8—1224no—
326C2×C8—1222no—
327C2×C8—2442no—
328C2×C8—2442no—
329C2×C8—2442no—
330C2×C8—2442no—
331C4⋊C4—22no—
332C4⋊C4—1224no—
333C4⋊C4—1224no—
334C4⋊C4—1224no—
335C4⋊C4—1222no—
336C42—1222no—
337C42—1222no—
338C42—1222no—
339C42—1222no—
340C42—2444no—
341C42—2444no—
342C23—611no—
343C23—611no—
344C23—611no—
345C23—611no—
346C23—611no—
347C23—611no—
348C23—1221no—
349C23—1221no—
350C23—1221no—
351C23—1221no—
352C23C2×C4×#692311yescharacteristic
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—612no—
356C2×C4—612no—
357C2×C4—611no—
358C2×C4—611no—
359C2×C4—612no—
360C2×C4—612no—
361C2×C4—612no—
362C2×C4—612no—
363C2×C4—612no—
364C2×C4—612no—
365C2×C4—612no—
366C2×C4—612no—
367C2×C4—612no—
368C2×C4—612no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1224no—
374C2×C4—1224no—
375C2×C4—1222no—
376C2×C4—1224no—
377C2×C4—1222no—
378C2×C4—1222no—
379C2×C4—1222no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4—2444no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2444no—
388C2×C4—2442no—
389C2×C4—2444no—
390C2×C4#1451985612yes—
391C2×C4D4×#692312yes—
392C2×C4D4×#692311yescharacteristic
393C2×C4Q8×#692311yescharacteristic
394C8—42no—
395C8—2444no—
396C8—2442no—
397C22—21no—
398C22—21no—
399C22—611no—
400C22—611no—
401C22—611no—
402C22—611no—
403C22—611no—
404C22—611no—
405C22—611no—
406C22—611no—
407C22—1221no—
408C22—1221no—
409C22—1221no—
410C22—1221no—
411C22—1221no—
412C22—1221no—
413C22—1221no—
414C22—1221no—
415C22—1221no—
416C22—1221no—
417C22#1684069811yescharacteristic
418C22C22⋊C4×#692311yescharacteristic
419C22C4⋊C4×#692311yescharacteristic
420C4—42no—
421C4—612no—
422C4—612no—
423C4—1222no—
424C4—1222no—
425C4—2442no—
426C4—2444no—
427C4—2442no—
428C4#1684071112yes—
429C4#1684071212yes—
430C2—21no—
431C2—21no—
432C2—611no—
433C2—611no—
434C2—611no—
435C2—611no—
436C2—1221no—
437C2—1221no—
438C2#2146099411yescharacteristic
439C2#100×#692311yescharacteristic
440C2#101×#692311yescharacteristic
subgroupG/H
centerC22C22⋊C4×#6923
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#343C4
socleC22×C61C4×C22⋊C4
prime radicalC23×D61C22×C4
cosocleC22×C4×D61C23
hypercenter#343#6923
hypocenterC61#10802
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
13. #16840642C4semidirect
19. #16839531C4semidirect
20. #16839530C4semidirect
21. C61×#343C4semidirect
239. #343#6923semidirect
242. C61#10802semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×#69232
#214615222
C2×#168406412
#214614812
#343×D612
#1080261