Finite Group Databasebeta

← #29580562

Subgroups — #29580562

Order 15616.

830 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16839918C211yesmaximal, characteristic, complemented
2#21451752C211yesmaximal, characteristic
3C2×#16839500C211yesmaximal, characteristic, complemented
4C2×#16839496C211yesmaximal, characteristic
5#21444090C211yesmaximal, characteristic, complemented
6#21443661C211yesmaximal, characteristic, complemented
7C2×C61×#448C211yesmaximal, characteristic
8C22×#11758202—21no—
9C2×#14519756C2211yescharacteristic
10#16839918—22no—
11#16839918—22no—
12C2×#14519701—21no—
13C2×C22⋊#92418C2211yescharacteristic
14#16839700—21no—
15#16839687—21no—
16#16839676—21no—
17#16839674—21no—
18#16839642—22no—
19C2×#14519684—22no—
20C2×#14519684C2211yescharacteristic
21C2×#14519684C2211yescharacteristic
22#16839500—22no—
23#16839496—22no—
24C23×Q8×C61C2211yescharacteristic
25C22×SD16×C61—21no—
26C2×#121×C61C2211yescharacteristic
27C61×#448—22no—
28C61×#448—22no—
29C2×#103×C61—21no—
30C2×C22⋊C8×C61C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C23×Dic61—21no—
33C23×Dic61D412yes—
34C2×#11758202—24no—
35C2×#11758202—44no—
36C22×#92418—21no—
37#14519756—21no—
38#14519756—21no—
39#14519756—21no—
40#14519756—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—22no—
45C2×C22⋊Dic61—22no—
46#14519701—24no—
47C22⋊#92418—21no—
48C22⋊#92418D412yes—
49#14519684—22no—
50#14519684—22no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—44no—
56C22×Q8×C61—21no—
57C22×Q8×C61—21no—
58C22×Q8×C61—21no—
59C22×Q8×C61—21no—
60C22×Q8×C61—21no—
61C22×Q8×C61—44no—
62C22×Q8×C61D412yes—
63C22×D4×C61—21no—
64C22×D4×C61D411yescharacteristic
65C23×C4×C61—21no—
66C23×C4×C61C2311yescharacteristic
67C2×SD16×C61—24no—
68C2×SD16×C61—44no—
69C22×C8×C61—21no—
70#121×C61—21no—
71#121×C61—21no—
72#121×C61—21no—
73#121×C61—21no—
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C22⋊C4×C61—21no—
76#103×C61—24no—
77C22⋊C8×C61—21no—
78C22⋊C8×C61D412yes—
79C24×C61—21no—
80C24×C61C2×D411yescharacteristic
81C2×Q8×C61—24no—
82C2×Q8×C61—24no—
83C2×Q8×C61—22no—
84C2×Q8×C61—22no—
85C2×Q8×C61—44no—
86C2×Q8×C61—42no—
87C2×Q8×C61—42no—
88C2×Q8×C61—44no—
89C2×Q8×C61—44no—
90C2×Q8×C61—44no—
91C2×Q8×C61—41no—
92C2×Q8×C61—41no—
93C2×D4×C61—21no—
94C2×D4×C61—21no—
95C2×D4×C61—42no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C2×D4×C61—42no—
99C2×D4×C61—42no—
100C22×C4×C61—24no—
101C22×C4×C61—22no—
102C22×C4×C61—21no—
103C22×C4×C61—42no—
104C22×C4×C61—42no—
105C22×C4×C61—41no—
106C22×C4×C61—41no—
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C22×Dic61—22no—
114C22×Dic61—22no—
115C22×Dic61—21no—
116C22×Dic61—21no—
117C22×Dic61—22no—
118C22×Dic61—22no—
119C22×Dic61—42no—
120C22×Dic61—42no—
121C22×Dic61—41no—
122C22×Dic61—42no—
123C22×Dic61—41no—
124C22×Dic61—42no—
125C2×Dic122—21no—
126C2×Dic122—21no—
127C2×Dic122—42no—
128SD16×C61—48no—
129C2×C8×C61—22no—
130C2×C8×C61—42no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C22⋊C4×C61—41no—
134C22⋊C4×C61—41no—
135C22⋊Dic61—41no—
136C22⋊Dic61—41no—
137C22⋊Dic61—82no—
138C22⋊Dic61—82no—
139#11758202—48no—
140C4⋊Dic61—21no—
141C4⋊Dic61—21no—
142#11758196—41no—
143#11758196—41no—
144C2×#92418—22no—
145C2×#92418—42no—
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—
159Q8×C61—24no—
160Q8×C61—24no—
161Q8×C61—42no—
162Q8×C61—42no—
163Q8×C61—44no—
164Q8×C61—44no—
165D4×C61—42no—
166D4×C61—81no—
167D4×C61—82no—
168D4×C61—81no—
169D4×C61—81no—
170C2×C4×C61—22no—
171C2×C4×C61—22no—
172C2×C4×C61—24no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—44no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×C4×C61—44no—
181C2×C4×C61—41no—
182C2×C4×C61—42no—
183C2×C4×C61#12011yescharacteristic
184C2×C4×C61#12011yescharacteristic
185C2×C4×C61#12111yescharacteristic
186C2×C4×C61#12111yescharacteristic
187C2×Dic61—44no—
188C2×Dic61—42no—
189C2×Dic61—44no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—42no—
193C2×Dic61—41no—
194C2×Dic61—42no—
195C2×Dic61—41no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—82no—
199C2×Dic61—81no—
200C2×Dic61—81no—
201C2×Dic61—82no—
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—44no—
233C4×C61—81no—
234Dic61—82no—
235Dic61—82no—
236Dic61—81no—
237Dic61—81no—
238C2×#451—611no—
239C2×#448D6111yescharacteristic
240#2639—611no—
241C2×#328—611no—
242C2×#327—611no—
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×Q8C2×D6111yescharacteristic
255C22×Q16—1221no—
256C22×SD16—21no—
257C2×C22⋊Q8—611no—
258C2×#121C2×D6111yescharacteristic
259#451—1222no—
260#451—1222no—
261#448—22no—
262#448—22no—
263C2×#103—21no—
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—611no—
274C2×#95—1222no—
275#328—1222no—
276#327—1222no—
277C61#996511yescharacteristic, complemented, Sylow
278C22×Q8—21no—
279C22×Q8—21no—
280C22×Q8—21no—
281C22×Q8—21no—
282C22×Q8—21no—
283C22×Q8—44no—
284C22×Q8—611no—
285C22×Q8C22⋊D6112yes—
286C22×D4—21no—
287C22×D4C22⋊D6111yescharacteristic
288C23×C4—21no—
289C23×C4—612no—
290C23×C4—1221no—
291C23×C4C22×D6111yescharacteristic
292C2×Q16—1224no—
293C2×Q16—2444no—
294C2×SD16—24no—
295C2×SD16—44no—
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⋊C4C22⋊D6111yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—1222no—
311C2×C22⋊C4—1222no—
312C2×C22⋊C4—1221no—
313#103—24no—
314#103—1224no—
315C22⋊C8—21no—
316C22⋊C8—612no—
317C22⋊C8—1221no—
318C22⋊C8C22⋊D6112yes—
319#95—1222no—
320#95—1222no—
321#95—1221no—
322#95—1221no—
323#95—1221no—
324#95—1221no—
325#95—2444no—
326C24—21no—
327C24D4×D6111yescharacteristic
328C2×Q8—24no—
329C2×Q8—24no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—44no—
333C2×Q8—42no—
334C2×Q8—42no—
335C2×Q8—44no—
336C2×Q8—44no—
337C2×Q8—44no—
338C2×Q8—41no—
339C2×Q8—41no—
340C2×Q8—1221no—
341C2×Q8—1221no—
342C2×Q8—2442no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—42no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—42no—
349C2×D4—42no—
350C22×C4—24no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—1222no—
358C22×C4—1222no—
359C22×C4—1222no—
360C22×C4—1221no—
361C22×C4—1221no—
362C22×C4—1222no—
363C22×C4—2442no—
364C22×C4—2441no—
365C22×C4—2441no—
366C22×C4—2442no—
367C22×C4—2442no—
368C22×C4—2442no—
369C22×C4D4×D6111yescharacteristic
370C22×C4D4×D6111yescharacteristic
371C22×C4#1175822411yescharacteristic
372C22×C4C2×C22⋊D6111yescharacteristic
373C22×C4C2×C22⋊D6111yescharacteristic
374C22×C4C2×C22⋊D6111yescharacteristic
375Q16—2448no—
376SD16—48no—
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#1451974511yescharacteristic
402C23#1451974911yescharacteristic
403C23#1451977311yescharacteristic
404C23#1451979812yes—
405C23#1451980612yes—
406Q8—24no—
407Q8—24no—
408Q8—42no—
409Q8—42no—
410Q8—44no—
411Q8—44no—
412Q8—4881no—
413Q8—2442no—
414D4—42no—
415D4—81no—
416D4—82no—
417D4—81no—
418D4—81no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—4881no—
433C2×C4—4882no—
434C2×C4—4881no—
435C2×C4—4882no—
436C2×C4—2444no—
437C2×C4—2442no—
438C2×C4—2444no—
439C2×C4—2441no—
440C2×C4—2442no—
441C2×C4—2441no—
442C2×C4—2442no—
443C2×C4—2442no—
444C2×C4—2442no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4#1451974511yescharacteristic
448C2×C4#1451974611yescharacteristic
449C2×C4#1451974811yescharacteristic
450C2×C4#1451974911yescharacteristic
451C8—42no—
452C8—2442no—
453C22—21no—
454C22—21no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—21no—
460C22—21no—
461C22—81no—
462C22—82no—
463C22—82no—
464C22—81no—
465C22—81no—
466C22#1683967011yescharacteristic
467C22#1683992112yes—
468C22#1683993811yescharacteristic
469C22#1683994311yescharacteristic
470C22#1683994812yes—
471C22#1683998212yes—
472C22#1684014311yescharacteristic
473C22#1684015311yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—44no—
479C4—81no—
480C4—4882no—
481C4—4881no—
482C4—4882no—
483C4—4881no—
484C2—21no—
485C2—22no—
486C2—21no—
487C2—161no—
488C2#2144477912yes—
489C2#2144479612yes—
490C2#2144686411yescharacteristic
491C2#2144691111yescharacteristic
492C2#2144694211yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#448C2
socleC23×C61#120
prime radicalC2×#121×C61C22
hypercenterC2×#448D61
hypocenterC61#9965
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#16839918C2semidirect
3. C2×#16839500C2semidirect
5. #21444090C2semidirect
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×#168399182
#214517522
C2×#168395002
C2×#168394962
#214440902
#214436612
C2×C61×#4482
#996561