Finite Group Databasebeta

← #29580564

Subgroups — #29580564

Order 15616.

830 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#16839920C211yesmaximal, characteristic, complemented
2C2×#16839900C211yesmaximal, characteristic
3#21451752C211yesmaximal, characteristic
4C2×#16839498C211yesmaximal, characteristic, complemented
5#21444089C211yesmaximal, characteristic, complemented
6#21443661C211yesmaximal, characteristic, complemented
7C2×C61×#327C211yesmaximal, characteristic
8C23×Dic122C2211yescharacteristic
9C22×Dic244—21no—
10C22×#11758200—21no—
11C2×#14519756C2211yescharacteristic
12#16839920—22no—
13#16839920—22no—
14#16839900—22no—
15#16839900—22no—
16C2×#14519702—21no—
17C2×#14519700—21no—
18C2×C22⋊#92418C2211yescharacteristic
19#16839700—21no—
20#16839687—21no—
21#16839676—21no—
22#16839674—21no—
23#16839642—22no—
24C2×#14519684—22no—
25C2×#14519684C2211yescharacteristic
26#16839498—22no—
27C2×#121×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×#95×C61C2211yescharacteristic
30C61×#327—22no—
31C22×Dic122—21no—
32C22×Dic122—21no—
33C22×Dic122—21no—
34C22×Dic122—21no—
35C22×Dic122—21no—
36C22×Dic122—44no—
37C22×Dic122D411yescharacteristic
38C22×Dic122D412yes—
39C23×Dic61—21no—
40C23×Dic61D412yes—
41C2×Dic244—24no—
42C2×Dic244—44no—
43C2×#11758200—24no—
44C2×#11758200—44no—
45C22×#92418—21no—
46#14519756—21no—
47#14519756—21no—
48#14519756—21no—
49#14519756—21no—
50C2×C4⋊Dic61D411yescharacteristic
51C2×#11758196—21no—
52C2×C22⋊Dic61—21no—
53C2×C22⋊Dic61—22no—
54C2×C22⋊Dic61—22no—
55#14519702—24no—
56#14519700—24no—
57C22⋊#92418—21no—
58C22⋊#92418D412yes—
59#14519684—22no—
60#14519684—22no—
61#14519684—21no—
62#14519684—21no—
63#14519684—44no—
64C22×D4×C61—21no—
65C22×D4×C61D411yescharacteristic
66C23×C4×C61—21no—
67C23×C4×C61C2311yescharacteristic
68C22×C8×C61—21no—
69#121×C61—21no—
70#121×C61—21no—
71#121×C61—21no—
72#121×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C22⋊C4×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61D412yes—
77#95×C61—21no—
78#95×C61—21no—
79C24×C61—21no—
80C24×C61C2×D411yescharacteristic
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—42no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—42no—
87C2×D4×C61—42no—
88C22×C4×C61—22no—
89C22×C4×C61—21no—
90C22×C4×C61—42no—
91C22×C4×C61—41no—
92C22×C4×C61—42no—
93C22×C4×C61—41no—
94C22×C4×C61—42no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61#4111yescharacteristic
101C22×Dic61—24no—
102C22×Dic61—22no—
103C22×Dic61—22no—
104C22×Dic61—21no—
105C22×Dic61—21no—
106C22×Dic61—22no—
107C22×Dic61—22no—
108C22×Dic61—42no—
109C22×Dic61—41no—
110C22×Dic61—41no—
111C22×Dic61—42no—
112C22×Dic61—42no—
113C2×Dic122—24no—
114C2×Dic122—24no—
115C2×Dic122—22no—
116C2×Dic122—22no—
117C2×Dic122—21no—
118C2×Dic122—21no—
119C2×Dic122—44no—
120C2×Dic122—44no—
121C2×Dic122—44no—
122C2×Dic122—44no—
123C2×Dic122—42no—
124C2×Dic122—42no—
125C2×Dic122—41no—
126C2×Dic122—41no—
127C2×Dic122—42no—
128C2×C8×C61—22no—
129C2×C8×C61—42no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C22⋊C4×C61—41no—
133C22⋊C4×C61—41no—
134C22⋊Dic61—41no—
135C22⋊Dic61—41no—
136C22⋊Dic61—82no—
137C22⋊Dic61—82no—
138#11758200—48no—
139C4⋊Dic61—21no—
140C4⋊Dic61—21no—
141#11758196—41no—
142#11758196—41no—
143C2×#92418—22no—
144C2×#92418—42no—
145Dic244—48no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—22no—
149C23×C61—41no—
150C23×C61—42no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61—42no—
154C23×C61#12011yescharacteristic
155C23×C61#12111yescharacteristic
156C23×C61#12711yescharacteristic
157C23×C61#13512yes—
158C23×C61#13712yes—
159D4×C61—42no—
160D4×C61—81no—
161D4×C61—82no—
162D4×C61—81no—
163D4×C61—81no—
164C2×C4×C61—22no—
165C2×C4×C61—22no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—44no—
171C2×C4×C61—42no—
172C2×C4×C61—41no—
173C2×C4×C61—42no—
174C2×C4×C61—82no—
175C2×C4×C61—81no—
176C2×C4×C61—81no—
177C2×C4×C61#12011yescharacteristic
178C2×C4×C61#12011yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×Dic61—24no—
182C2×Dic61—42no—
183C2×Dic61—44no—
184C2×Dic61—42no—
185C2×Dic61—44no—
186C2×Dic61—44no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—42no—
190C2×Dic61—41no—
191C2×Dic61—42no—
192C2×Dic61—41no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—82no—
196Dic122—24no—
197Dic122—24no—
198Dic122—42no—
199Dic122—42no—
200Dic122—44no—
201Dic122—44no—
202Dic122—42no—
203Dic122—81no—
204C8×C61—42no—
205#92418—42no—
206#9965—611nomaximal, Sylow
207C22×C61—22no—
208C22×C61—22no—
209C22×C61—22no—
210C22×C61—22no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—82no—
216C22×C61—82no—
217C22×C61—81no—
218C22×C61—81no—
219C22×C61—81no—
220C22×C61#39211yescharacteristic
221C22×C61#45212yes—
222C22×C61#45511yescharacteristic
223C22×C61#45611yescharacteristic
224C22×C61B(4,𝔽2)12yes—
225C22×C61#46412yes—
226C22×C61#49511yescharacteristic
227C22×C61#49711yescharacteristic
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—82no—
233C4×C61—81no—
234Dic61—44no—
235Dic61—82no—
236Dic61—81no—
237Dic61—81no—
238C2×#451—611no—
239C2×#448—611no—
240#2639—611no—
241C2×#328—611no—
242C2×#327D6111yescharacteristic
243#1446—611no—
244#1280—611no—
245C2×C61—21no—
246C2×C61—22no—
247C2×C61—21no—
248C2×C61—161no—
249C2×C61#160312yes—
250C2×C61#160612yes—
251C2×C61#200711yescharacteristic
252C2×C61#201511yescharacteristic
253C2×C61#202111yescharacteristic
254C23×Q8—611no—
255C22×Q16—1221no—
256C22×SD16—1221no—
257C2×C22⋊Q8—611no—
258C2×#121C2×D6111yescharacteristic
259#451—1222no—
260#451—1222no—
261#448—1222no—
262#448—1222no—
263C2×#103—1221no—
264C2×#103—1221no—
265C2×C22⋊C8—611no—
266C2×C22⋊C8C2×D6111yescharacteristic
267#400—1221no—
268#397—1221no—
269#394—1221no—
270#393—1221no—
271#386—1222no—
272C2×#95—611no—
273C2×#95—1222no—
274C2×#95C2×D6111yescharacteristic
275#328—1222no—
276#327—22no—
277C61#996511yescharacteristic, complemented, Sylow
278C22×Q8—611no—
279C22×Q8—612no—
280C22×Q8—1221no—
281C22×Q8—1221no—
282C22×Q8—1221no—
283C22×Q8—1221no—
284C22×Q8—1221no—
285C22×Q8—2444no—
286C22×D4—21no—
287C22×D4D24411yescharacteristic
288C23×C4—21no—
289C23×C4—612no—
290C23×C4—1221no—
291C23×C4C22×D6111yescharacteristic
292C2×Q16—1224no—
293C2×Q16—2444no—
294C2×SD16—1224no—
295C2×SD16—2444no—
296C22×C8—21no—
297C22×C8—1221no—
298C22⋊Q8—1221no—
299C22⋊Q8—1221no—
300C22⋊Q8—1221no—
301C22⋊Q8—1221no—
302#121—21no—
303#121—21no—
304#121—21no—
305#121—21no—
306C2×C4⋊C4—611no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4D24411yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—1222no—
311C2×C22⋊C4—1222no—
312C2×C22⋊C4—1221no—
313#103—1224no—
314#103—1224no—
315C22⋊C8—21no—
316C22⋊C8—612no—
317C22⋊C8—1221no—
318C22⋊C8C22⋊D6112yes—
319#95—21no—
320#95—21no—
321#95—1222no—
322#95—1222no—
323#95—1221no—
324#95—1221no—
325#95—2444no—
326C24—21no—
327C24D4×D6111yescharacteristic
328C2×Q8—1224no—
329C2×Q8—1224no—
330C2×Q8—1222no—
331C2×Q8—1221no—
332C2×Q8—1222no—
333C2×Q8—1221no—
334C2×Q8—2442no—
335C2×Q8—2442no—
336C2×Q8—2442no—
337C2×Q8—2444no—
338C2×Q8—2444no—
339C2×Q8—2444no—
340C2×Q8—2444no—
341C2×Q8—2441no—
342C2×Q8—2441no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—42no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—42no—
349C2×D4—42no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—42no—
357C22×C4—1224no—
358C22×C4—1222no—
359C22×C4—1222no—
360C22×C4—1222no—
361C22×C4—1221no—
362C22×C4—1221no—
363C22×C4—1222no—
364C22×C4—2442no—
365C22×C4—2442no—
366C22×C4—2442no—
367C22×C4—2441no—
368C22×C4—2441no—
369C22×C4C2×D24411yescharacteristic
370C22×C4#1175822211yescharacteristic
371C22×C4D4×D6111yescharacteristic
372C22×C4D4×D6111yescharacteristic
373C22×C4D4×D6111yescharacteristic
374C22×C4C2×C22⋊D6111yescharacteristic
375Q16—2448no—
376SD16—2448no—
377C2×C8—22no—
378C2×C8—42no—
379C2×C8—1222no—
380C2×C8—2442no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—1221no—
384C4⋊C4—1221no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—4882no—
390C22⋊C4—4882no—
391C22⋊C4—2441no—
392C22⋊C4—2441no—
393C23—21no—
394C23—21no—
395C23—22no—
396C23—41no—
397C23—41no—
398C23—42no—
399C23—42no—
400C23—41no—
401C23#1451974711yescharacteristic
402C23#1451975011yescharacteristic
403C23#1451977311yescharacteristic
404C23#1451979612yes—
405C23#1451980612yes—
406Q8—1224no—
407Q8—1224no—
408Q8—4881no—
409Q8—2442no—
410Q8—2442no—
411Q8—2442no—
412Q8—2444no—
413Q8—2444no—
414D4—42no—
415D4—81no—
416D4—82no—
417D4—81no—
418D4—81no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—81no—
430C2×C4—82no—
431C2×C4—81no—
432C2×C4—1224no—
433C2×C4—4882no—
434C2×C4—2444no—
435C2×C4—2441no—
436C2×C4—2442no—
437C2×C4—2441no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2442no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2444no—
444C2×C4—2442no—
445C2×C4—2444no—
446C2×C4—2442no—
447C2×C4#1451974511yescharacteristic
448C2×C4#1451974711yescharacteristic
449C2×C4#1451975011yescharacteristic
450C2×C4#1451975111yescharacteristic
451C8—42no—
452C8—2442no—
453C22—21no—
454C22—21no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—21no—
460C22—21no—
461C22—81no—
462C22—81no—
463C22—82no—
464C22—82no—
465C22—81no—
466C22#1683967111yescharacteristic
467C22#1683992512yes—
468C22#1683994111yescharacteristic
469C22#1683994611yescharacteristic
470C22#1683995012yes—
471C22#1683998312yes—
472C22#1684014511yescharacteristic
473C22#1684015311yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—82no—
479C4—81no—
480C4—4881no—
481C4—4882no—
482C4—4881no—
483C4—2444no—
484C2—21no—
485C2—22no—
486C2—21no—
487C2—161no—
488C2#2144478312yes—
489C2#2144480012yes—
490C2#2144686711yescharacteristic
491C2#2144691511yescharacteristic
492C2#2144694411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#327C2
socleC23×C61#120
prime radicalC2×#121×C61C22
hypercenterC2×#327D61
hypocenterC61#9965
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
1. C2×#16839920C2semidirect
4. C2×#16839498C2semidirect
5. #21444089C2semidirect
6. #21443661C2semidirect
277. C61#9965semidirect

Maximal subgroups

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

subgroupindex
C2×#168399202
C2×#168399002
#214517522
C2×#168394982
#214440892
#214436612
C2×C61×#3272
#996561