Finite Group Databasebeta

← #29587311

Subgroups — #29587311

Order 15616.

910 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519709C211yesmaximal, characteristic, complemented
2C2×#16839764C212yesmaximal
3C2×#16839728C211yesmaximal, characteristic
4C2×#16839530C212yesmaximal, complemented
5C2×C61×#341C211yesmaximal, characteristic, complemented
6C22×#11758222C2211yescharacteristic
7C22×#11758194C2211yescharacteristic
8C22×C4⋊Dic61C2212yes—
9C2×#14519709—24no—
10C2×#14519709—22no—
11#16839764—24no—
12#16839764—24no—
13C2×#14519702—22no—
14C2×#14519699—22no—
15#16839728—22no—
16#16839728C414yescomplemented
17C2×#14519689—22no—
18#16839530—24no—
19C22×M16×C61C2212yes—
20C23×C8×C61C2211yescharacteristic
21C61×#341—22no—
22C2×#11758222—21no—
23C2×#11758222—21no—
24C2×#11758222—22no—
25C2×#11758222—22no—
26C2×#11758222—22no—
27C2×#11758222—22no—
28C2×#11758222C2×C412yes—
29C2×#11758222Q812yes—
30C22×Dic122D411yescharacteristic
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C23×Dic61—22no—
34C22×C4×D61—21no—
35C2×#11758194—21no—
36C2×#11758194—22no—
37C2×#11758194—22no—
38C2×#11758194C2×C412yes—
39C22×#92418—21no—
40C2×C4⋊Dic61—22no—
41C2×C4⋊Dic61—22no—
42C2×C4⋊Dic61—22no—
43C2×C4⋊Dic61—22no—
44C2×C4⋊Dic61—22no—
45C2×C4⋊Dic61D414yes—
46#14519709—28no—
47#14519702—28no—
48#14519699—28no—
49#14519689—28no—
50C23×C4×C61C2311yescharacteristic
51C2×M16×C61—22no—
52C2×M16×C61—22no—
53C2×M16×C61—22no—
54C2×M16×C61—22no—
55C2×M16×C61—22no—
56C2×M16×C61D414yes—
57C22×C8×C61—22no—
58C22×C8×C61—22no—
59C22×C8×C61—22no—
60C22×C8×C61C2×C412yes—
61C22×C8×C61D412yes—
62C22×C8×C61D412yes—
63C24×C61#4111yescharacteristic
64C23×D61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D412yes—
70C22×C4×C61C2×D412yes—
71C22×C4×C61C2×Q811yescharacteristic
72C22×C4×C61#4112yes—
73C22×C4×C61#4112yes—
74C22×C4×C61#4111yescharacteristic
75C2×C22⋊D61—22no—
76C2×C22⋊D61—22no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C22×Dic61—21no—
80C22×Dic61—24no—
81C22×Dic61—42no—
82C22×Dic61—42no—
83C22×Dic61—84no—
84#11758222—24no—
85#11758222—24no—
86#11758222—24no—
87#11758222—24no—
88#11758222—42no—
89#11758222—42no—
90#11758222—42no—
91#11758222—42no—
92C2×D244—22no—
93C2×D244—22no—
94C2×D244—21no—
95C2×D244C4⋊C412yes—
96C2×C4×D61—22no—
97C2×C4×D61—22no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×Dic122—22no—
103C2×Dic122—22no—
104C2×Dic122—21no—
105C2×Dic122C4⋊C412yes—
106M16×C61—24no—
107M16×C61—24no—
108M16×C61—42no—
109M16×C61—42no—
110C2×C8×C61—24no—
111C2×C8×C61—22no—
112C2×C8×C61—24no—
113C2×C8×C61—22no—
114C2×C8×C61—24no—
115C2×C8×C61—42no—
116C2×C8×C61—42no—
117C2×C8×C61C22⋊C414yes—
118C4⋊Dic61—24no—
119C4⋊Dic61—24no—
120C4⋊Dic61—42no—
121C4⋊Dic61—42no—
122#11758194—24no—
123#11758194—42no—
124C2×#92418—22no—
125C2×#92418—41no—
126C2×#92418—41no—
127C23×C61—24no—
128C23×C61#11711yescharacteristic
129C23×C61#12112yes—
130C23×C61#12111yescharacteristic
131C23×C61C22⋊Q811yescharacteristic
132C23×C61#12612yes—
133C22×D61—22no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—44no—
137C2×C4×C61C2×C22⋊C411yescharacteristic
138C2×C4×C61C2×C4⋊C411yescharacteristic
139C2×C4×C61C4×D412yes—
140C2×C4×C61C4×D412yes—
141C2×C4×C61#12012yes—
142C2×C4×C61#12011yescharacteristic
143C2×C4×C61#12112yes—
144C2×C4×C61#12112yes—
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61C22⋊Q812yes—
147C2×C4×C61C22⋊Q812yes—
148C2×C4×C61C22⋊Q811yescharacteristic
149C2×C4×C61#12312yes—
150C2×C4×C61#12311yescharacteristic
151C2×C4×C61#12312yes—
152C2×C4×C61#12411yescharacteristic
153C2×C4×C61#12412yes—
154C2×C4×C61#12711yescharacteristic
155C22⋊D61—44no—
156C22⋊D61—44no—
157C2×Dic61—22no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—44no—
161C2×Dic61—84no—
162C2×Dic61—84no—
163C2×Dic61—84no—
164D244—24no—
165D244—42no—
166C4×D61—42no—
167C4×D61—42no—
168C4×D61—42no—
169C4×D61—42no—
170Dic122—24no—
171Dic122—42no—
172C8×C61—24no—
173C8×C61—44no—
174#92418—42no—
175#11106—611nomaximal, Sylow
176C22×C61—22no—
177C22×C61—22no—
178C22×C61—24no—
179C22×C61—22no—
180C22×C61—22no—
181C22×C61#38011yescharacteristic
182C22×C61#38812yes—
183C22×C61#39211yescharacteristic
184C22×C61#39612yes—
185C22×C61#39711yescharacteristic
186C22×C61#47114yes—
187C2×D61—44no—
188C2×D61—42no—
189C2×D61—82no—
190C2×D61—82no—
191C4×C61#38512yes—
192C4×C61#38611yescharacteristic
193C4×C61#39011yescharacteristic
194C4×C61#39311yescharacteristic
195C4×C61#39412yes—
196C4×C61#39911yescharacteristic
197Dic61—42no—
198Dic61—84no—
199C22×#106—611no—
200C2×#417—612no—
201C2×#408—611no—
202C2×#343—612no—
203C2×#341D6111yescharacteristic, complemented
204C2×C61—22no—
205C2×C61—22no—
206C2×C61#143911yescharacteristic
207C2×C61#181512yes—
208C2×C61#201912yes—
209C2×C61#207912yes—
210D61—82no—
211C22×#41—611no—
212C22×M16—611no—
213C22×M16C2×D6112yes—
214C23×C8C2×D6111yescharacteristic
215C22×C4⋊C4—612no—
216C2×#106—1224no—
217C2×#106—1222no—
218#417—1224no—
219#417—1224no—
220C2×#103—1222no—
221C2×#102—1222no—
222#408—614no—
223#408—1222no—
224C2×C22⋊C8—1222no—
225#343—1224no—
226#341—22no—
227C61#1110611yescharacteristic, complemented, Sylow
228C2×#41—612no—
229C2×#41—612no—
230C2×#41—1221no—
231C2×#41—1221no—
232C2×#41—1222no—
233C2×#41—1222no—
234C2×#41—1222no—
235C2×#41—1222no—
236C22×Q8—611no—
237C22×D4—611no—
238C22×D4—1221no—
239C23×C4—1221no—
240C23×C4—1222no—
241C23×C4C22×D6111yescharacteristic
242C2×M16—22no—
243C2×M16—22no—
244C2×M16—22no—
245C2×M16—22no—
246C2×M16—22no—
247C2×M16—612no—
248C2×M16—1221no—
249C2×M16—1222no—
250C2×M16—1222no—
251C2×M16D24414yes—
252C22×C8—22no—
253C22×C8—22no—
254C22×C8—22no—
255C22×C8—1221no—
256C22×C8C4×D6112yes—
257C22×C8D24412yes—
258C22×C8C22⋊D6112yes—
259C2×C4⋊C4—614no—
260C2×C4⋊C4—1222no—
261C2×C4⋊C4—1222no—
262C2×C4⋊C4—1222no—
263C2×C4⋊C4—1222no—
264C2×C4⋊C4—1222no—
265#106—1228no—
266#103—1228no—
267#102—1228no—
268C22⋊C8—1228no—
269C24—1221no—
270C24#1175822611yescharacteristic
271#41—1224no—
272#41—1224no—
273#41—1224no—
274#41—1224no—
275#41—2442no—
276#41—2442no—
277#41—2442no—
278#41—2442no—
279C2×Q8—612no—
280C2×Q8—1221no—
281C2×Q8—1222no—
282C2×Q8—1222no—
283C2×D4—612no—
284C2×D4—1222no—
285C2×D4—1222no—
286C2×D4—1222no—
287C2×D4—1221no—
288C2×D4—1222no—
289C2×D4—2442no—
290C2×D4—2442no—
291C22×C4—1221no—
292C22×C4—1222no—
293C22×C4—1222no—
294C22×C4—1224no—
295C22×C4—4884no—
296C22×C4—2442no—
297C22×C4—2442no—
298C22×C4—2441no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4C2×C4×D6111yescharacteristic
303C22×C4C2×D24411yescharacteristic
304C22×C4C2×D24412yes—
305C22×C4#1175822212yes—
306C22×C4D4×D6111yescharacteristic
307C22×C4D4×D6112yes—
308C22×C4#1175822412yes—
309C22×C4#1175822411yescharacteristic
310C22×C4Q8×D6111yescharacteristic
311C22×C4C2×C22⋊D6111yescharacteristic
312M16—24no—
313M16—24no—
314M16—42no—
315M16—42no—
316M16—1224no—
317M16—2442no—
318C2×C8—24no—
319C2×C8—22no—
320C2×C8—24no—
321C2×C8—22no—
322C2×C8—24no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—1222no—
326C2×C8—2441no—
327C2×C8—2441no—
328C2×C8#1175819814yes—
329C4⋊C4—1224no—
330C4⋊C4—1224no—
331C4⋊C4—2442no—
332C4⋊C4—2442no—
333C23—24no—
334C23—1222no—
335C23—2441no—
336C23—2444no—
337C23—2441no—
338C23#1451973511yescharacteristic
339C23#1451975212yes—
340C23#1451975211yescharacteristic
341C23#1451975311yescharacteristic
342C23#1451977212yes—
343Q8—1224no—
344Q8—2442no—
345D4—1224no—
346D4—2444no—
347D4—2444no—
348D4—2442no—
349C2×C4—1222no—
350C2×C4—4884no—
351C2×C4—4884no—
352C2×C4—4884no—
353C2×C4—2444no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2442no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4C2×#1175819811yescharacteristic
361C2×C4C4⋊C4×D6111yescharacteristic
362C2×C4#1451973712yes—
363C2×C4C4×D24412yes—
364C2×C4#1451974712yes—
365C2×C4#1451974711yescharacteristic
366C2×C4#1451974811yescharacteristic
367C2×C4#1451974912yes—
368C2×C4#1451975112yes—
369C2×C4#1451975512yes—
370C2×C4#1451975712yes—
371C2×C4#1451975711yescharacteristic
372C2×C4#1451975912yes—
373C2×C4#1451976111yescharacteristic
374C2×C4#1451976112yes—
375C2×C4#1451976312yes—
376C2×C4#1451976511yescharacteristic
377C2×C4#1451977411yescharacteristic
378C8—24no—
379C8—44no—
380C8—2442no—
381C22—22no—
382C22—22no—
383C22—24no—
384C22—22no—
385C22—22no—
386C22—4882no—
387C22—4882no—
388C22—2442no—
389C22—2444no—
390C22#1683961911yescharacteristic
391C22#1683965412yes—
392C22#1683967211yescharacteristic
393C22#1683968412yes—
394C22#1683968911yescharacteristic
395C22#1684002614yes—
396C4—4884no—
397C4—2442no—
398C4#1683963612yes—
399C4#1683963911yescharacteristic
400C4#1683966411yescharacteristic
401C4#1683967511yescharacteristic
402C4#1683967812yes—
403C4#1683969911yescharacteristic
404C2—22no—
405C2—22no—
406C2—4882no—
407C2#2144406511yescharacteristic
408C2#2144587512yes—
409C2#2144693612yes—
410C2#2144726612yes—
subgroupG/H
centerC23#14519752
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#341C2
socleC23×C61#121
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#341D61
hypocenterC61#11106
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
1. C22×#14519709C2semidirect
4. C2×#16839530C2semidirect
5. C2×C61×#341C2semidirect
16. #16839728C4semidirect
203. C2×#341D61semidirect
227. C61#11106semidirect

Maximal subgroups

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

subgroupindex
C22×#145197092
C2×#168397642
C2×#168397282
C2×#168395302
C2×C61×#3412
#1110661