Finite Group Databasebeta

← #29575650

Subgroups — #29575650

Order 15616.

588 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839814C211yesmaximal, characteristic
2#21454166C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic
4C2×#16839511C211yesmaximal, characteristic, complemented
5#21443703C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C2×C61×#333C211yesmaximal, characteristic, complemented
8C2×#14519753C412yes—
9C2×C42×D61C2211yescharacteristic
10#16839814—22no—
11#16839814—22no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519689—21no—
15C2×#14519689—21no—
16C2×C8×Dic61—21no—
17#16839669C412yes—
18#16839658—21no—
19#16839658—21no—
20#16839632C2211yescharacteristic
21#16839619—21no—
22#16839619—21no—
23#16839516—21no—
24#16839511—22no—
25C2×C4⋊Q8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C61×#333—22no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×#92418—21no—
33C22×#92418—21no—
34#14519753—44no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C412yes—
38C2×#11758196—22no—
39C2×#11758198—22no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C42×D61—21no—
44C42×D61—21no—
45C42×D61—21no—
46C42×D61—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50C4⋊#92418D412yes—
51#14519689—24no—
52#14519689—42no—
53C8×Dic61—24no—
54#14519684—22no—
55#14519684—22no—
56C22×Q8×C61C2×C412yes—
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59C4⋊Q8×C61—21no—
60C4⋊Q8×C61—21no—
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61D412yes—
70C23×D61C22⋊C411yescharacteristic
71C2×Q8×C61—22no—
72C2×Q8×C61—22no—
73C2×Q8×C61—42no—
74C2×Q8×C61—42no—
75C22×C4×C61—22no—
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61—22no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—22no—
96C2×C4×D61—41no—
97C2×C4×D61SD1612yes—
98C2×C4×D61Q1612yes—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61#4111yescharacteristic
112C42×C61#4111yescharacteristic
113#11758198—44no—
114C4⋊Dic61—41no—
115C4⋊Dic61—41no—
116C4⋊Dic61—41no—
117C4⋊Dic61—41no—
118C4⋊Dic61—42no—
119#11758196—44no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C2×#92418—22no—
127C2×#92418—41no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C23×C61C2×C22⋊C411yescharacteristic
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61#10312yes—
140Q8×C61—82no—
141Q8×C61—82no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—42no—
145C2×C4×C61—42no—
146C2×C4×C61—42no—
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61#12011yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12311yescharacteristic
153C2×C4×C61C2×SD1611yescharacteristic
154C2×C4×C61C2×Q1611yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61#13511yescharacteristic
157C2×C4×C61#13511yescharacteristic
158C2×C4×C61#13511yescharacteristic
159C2×C4×C61#13711yescharacteristic
160C2×C4×C61#13711yescharacteristic
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—42no—
169C2×Dic61—42no—
170C2×Dic61—42no—
171C2×Dic61#10012yes—
172C2×Dic61#10312yes—
173C4×D61—22no—
174C4×D61—22no—
175C4×D61—22no—
176C4×D61—22no—
177C4×D61—42no—
178C4×D61—42no—
179C4×D61—41no—
180C4×D61—41no—
181C4×D61—41no—
182C4×D61—41no—
183C8×C61—42no—
184C8×C61—81no—
185#92418—42no—
186#92418—81no—
187#9128—611nomaximal, Sylow
188C22×C61#38611yescharacteristic
189C22×C61C2×#10011yescharacteristic
190C22×C61#41311yescharacteristic
191C22×C61C2×#10311yescharacteristic
192C22×C61#41611yescharacteristic
193C22×C61#41611yescharacteristic
194C22×C61#41911yescharacteristic
195C2×D61—22no—
196C2×D61—22no—
197C2×D61—22no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—41no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—82no—
205C4×C61#45211yescharacteristic
206C4×C61#45211yescharacteristic
207C4×C61#46511yescharacteristic
208C4×C61#46511yescharacteristic
209C4×C61#46711yescharacteristic
210C4×C61#46711yescharacteristic
211C4×C61#48511yescharacteristic
212C4×C61#48511yescharacteristic
213Dic61—22no—
214Dic61—22no—
215Dic61—41no—
216Dic61—82no—
217C2×#431—611no—
218#2857—611no—
219#1797—611no—
220C2×#333—611no—
221C2×#333D6111yescharacteristic, complemented
222#1296—611no—
223#1296—611no—
224C2×C61#154211yescharacteristic
225C2×C61#154311yescharacteristic
226C2×C61#154811yescharacteristic
227C2×C61#155411yescharacteristic
228C2×C61#187311yescharacteristic
229C2×C61#189211yescharacteristic
230C2×C61#190011yescharacteristic
231D61—42no—
232C2×C4⋊Q8C2×D6111yescharacteristic
233C2×C22⋊Q8—612no—
234C22×C42—611no—
235#431—1222no—
236#431—1222no—
237C2×C4⋊C8—611no—
238C2×C4⋊C8—611no—
239C2×C4⋊C8C2×D6111yescharacteristic
240C2×C4⋊C8C2×D6111yescharacteristic
241C2×C22⋊C8—1221no—
242C2×C22⋊C8—1221no—
243C2×C4×C8—1221no—
244#391—612no—
245#389—1221no—
246#389—1221no—
247#384—611no—
248#380—1221no—
249#380—1221no—
250#336—1221no—
251#333—22no—
252#333—1222no—
253C61#912811yescharacteristic, complemented, Sylow
254C22×Q8C4×D6112yes—
255C23×C4—611no—
256C23×C4—611no—
257C23×C4—611no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—1221no—
261C22×C8—1221no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C22⋊Q8—2444no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—612no—
270C2×C4⋊C4—1222no—
271C2×C4⋊C4—1221no—
272C2×C4⋊C4—1221no—
273C2×C22⋊C4—1222no—
274C2×C42—611no—
275C2×C42—611no—
276C2×C42—611no—
277C2×C42—1221no—
278C2×C42—1221no—
279C2×C42—1221no—
280C2×C42—1221no—
281C2×C42C22×D6111yescharacteristic
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—612no—
286C4⋊C8—1221no—
287C4⋊C8—1221no—
288C4⋊C8—1221no—
289C4⋊C8C22⋊D6112yes—
290C22⋊C8—1224no—
291C22⋊C8—2442no—
292C4×C8—1224no—
293#95—1222no—
294#95—1222no—
295C24—611no—
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—42no—
299C2×Q8—42no—
300C22×C4—22no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—612no—
304C22×C4—612no—
305C22×C4—611no—
306C22×C4—1222no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1222no—
320C22×C4—2441no—
321C22×C4C2×C4×D6111yescharacteristic
322C22×C4D4×D6111yescharacteristic
323C22×C4D4×D6111yescharacteristic
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—1222no—
331C2×C8—2441no—
332C2×C8—2441no—
333C2×C8—2441no—
334C2×C8—2441no—
335C2×C8—2441no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—2442no—
341C4⋊C4—2444no—
342C4⋊C4—2441no—
343C4⋊C4—2441no—
344C4⋊C4—2441no—
345C4⋊C4—2441no—
346C22⋊C4—2444no—
347C42—1221no—
348C42—1221no—
349C42—1221no—
350C42—1221no—
351C42—1221no—
352C42—1221no—
353C42#1175822211yescharacteristic
354C42D4×D6111yescharacteristic
355C42#1175822411yescharacteristic
356C42C2×C22⋊D6111yescharacteristic
357C23—612no—
358C23—1221no—
359C23—1221no—
360C23—1221no—
361C23—1221no—
362C23—1221no—
363C23—1221no—
364C23C22⋊C4×D6111yescharacteristic
365Q8—82no—
366Q8—82no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—612no—
373C2×C4—612no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1222no—
379C2×C4—1222no—
380C2×C4—1222no—
381C2×C4—1222no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4#1451973711yescharacteristic
395C2×C4C4×C22⋊D6111yescharacteristic
396C2×C4#1451974511yescharacteristic
397C2×C4#1451974811yescharacteristic
398C2×C4#1451975011yescharacteristic
399C2×C4#1451975911yescharacteristic
400C2×C4SD16×D6111yescharacteristic
401C2×C4Q16×D6111yescharacteristic
402C2×C4#1451979811yescharacteristic
403C2×C4#1451979811yescharacteristic
404C2×C4#1451980011yescharacteristic
405C2×C4#1451980011yescharacteristic
406C2×C4#1451980611yescharacteristic
407C2×C4#1451980911yescharacteristic
408C8—42no—
409C8—81no—
410C8—4881no—
411C8—2442no—
412C22—1222no—
413C22—1222no—
414C22—1222no—
415C22—2441no—
416C22—2441no—
417C22—2441no—
418C22—2441no—
419C22#1683963811yescharacteristic
420C22#100×D6111yescharacteristic
421C22#1683974311yescharacteristic
422C22#103×D6111yescharacteristic
423C22#1683975711yescharacteristic
424C22#1683975711yescharacteristic
425C22#1683976911yescharacteristic
426C4—21no—
427C4—21no—
428C4—82no—
429C4—1222no—
430C4—1222no—
431C4—4882no—
432C4—2441no—
433C4#1683992111yescharacteristic
434C4#1683992311yescharacteristic
435C4#1683998811yescharacteristic
436C4#1683999411yescharacteristic
437C4#1684000011yescharacteristic
438C4#1684000211yescharacteristic
439C4#1684010111yescharacteristic
440C4#1684010211yescharacteristic
441C2—2442no—
442C2#2144447311yescharacteristic
443C2#2144448011yescharacteristic
444C2#2144449811yescharacteristic
445C2#2144452811yescharacteristic
446C2#2144612811yescharacteristic
447C2#2144623911yescharacteristic
448C2#2144627911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#333C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenterC2×#333D61
hypocenterC61#9128
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
4. C2×#16839511C2semidirect
5. #21443703C2semidirect
6. #21443703C2semidirect
7. C2×C61×#333C2semidirect
221. C2×#333D61semidirect
253. C61#9128semidirect

Maximal subgroups

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

subgroupindex
C2×#168398142
#214541662
#214457962
C2×#168395112
#214437032
C2×C61×#3332
#912861