Finite Group Databasebeta

← #29598294

Subgroups — #29598294

Order 15616.

536 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#21450124C211yesmaximal, characteristic
2C2×#16839553C211yesmaximal, characteristic
3C2×#16839552C211yesmaximal, characteristic
4C2×#16839551C211yesmaximal, characteristic
5#21445805C211yesmaximal, characteristic
6#100×Dic61C211yesmaximal, characteristic
7C2×C61×#352C211yesmaximal, characteristic
8C2×#14519758C2211yescharacteristic
9C2×D4×Dic61C2211yescharacteristic
10C22×#11758196C411yescharacteristic, complemented
11C2×#14519694C2211yescharacteristic
12C2×#14519692C2211yescharacteristic
13M16×Dic61—21no—
14#16839695—21no—
15#16839690—21no—
16#16839657—21no—
17#16839625C411yescharacteristic, complemented
18#16839623C411yescharacteristic, complemented
19#16839620—21no—
20#16839620—21no—
21#16839620C411yescharacteristic, complemented
22#16839553—22no—
23#16839552—22no—
24#16839551—22no—
25#16839530—21no—
26#16839528—21no—
27C2×#123×C61C2211yescharacteristic
28C2×#100×C61C2211yescharacteristic
29C2×#99×C61C2211yescharacteristic
30C61×#352—22no—
31C23×Dic61C2×C411yescharacteristic
32C23×Dic61C2×C411yescharacteristic
33C23×Dic61D411yescharacteristic
34C2×#11758194—21no—
35#14519758—21no—
36#14519758—21no—
37#14519758—21no—
38#14519758—21no—
39D4×Dic61—41no—
40D4×Dic61—41no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758196—41no—
47C2×#11758196—41no—
48C2×#11758196—41no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61C2×C411yescharacteristic
52C2×C22⋊Dic61C2×C411yescharacteristic
53C2×C22⋊Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55#14519694—21no—
56#14519694D412yes—
57#14519692—21no—
58#14519692—21no—
59#14519687—41no—
60C8×Dic61—41no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66#14519684—41no—
67C22×D4×C61C2311yescharacteristic
68C23×C4×C61C2×C411yescharacteristic
69C2×M16×C61—21no—
70#123×C61—21no—
71#123×C61—21no—
72#123×C61—21no—
73#123×C61—21no—
74C2×C4⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61—21no—
77C2×C22⋊C4×C61C2×C411yescharacteristic
78#100×C61—21no—
79#100×C61D412yes—
80#99×C61—21no—
81#99×C61—21no—
82C24×C61C22×C411yescharacteristic
83C24×C61C2×D411yescharacteristic
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61C2×D411yescharacteristic
87C2×D4×C61C2×D411yescharacteristic
88C2×D4×C61#4111yescharacteristic
89C2×D4×C61#4111yescharacteristic
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61C2×D411yescharacteristic
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—21no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61—21no—
106C22×Dic61—42no—
107C22×Dic61—42no—
108C22×Dic61—41no—
109C22×Dic61—41no—
110C22×Dic61—41no—
111C22×Dic61C22⋊C411yescharacteristic
112C22×Dic61C22⋊C411yescharacteristic
113C22×Dic61C22⋊C411yescharacteristic
114C22×Dic61C22⋊C411yescharacteristic
115M16×C61—22no—
116M16×C61—41no—
117C2×C8×C61—41no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C22⋊C4×C61—21no—
121C22⋊C4×C61—21no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C22⋊C4×C61—41no—
126C22⋊Dic61—21no—
127C22⋊Dic61—21no—
128C22⋊Dic61—41no—
129C22⋊Dic61—41no—
130C22⋊Dic61—41no—
131C22⋊Dic61—41no—
132C22⋊Dic61—41no—
133C22⋊Dic61—41no—
134C4⋊Dic61—41no—
135#11758196—42no—
136#11758196—42no—
137#11758196—41no—
138#11758196—41no—
139#11758196—41no—
140#11758196—41no—
141#11758196—82no—
142C4×Dic61—21no—
143C4×Dic61—21no—
144#11758194—22no—
145#11758194—41no—
146C2×#92418—41no—
147C23×C61—21no—
148C23×C61—21no—
149C23×C61—21no—
150C23×C61—21no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61C2×C22⋊C411yescharacteristic
156C23×C61C4×D411yescharacteristic
157C23×C61C4×D411yescharacteristic
158C23×C61#12411yescharacteristic
159C23×C61#12711yescharacteristic
160D4×C61—41no—
161D4×C61—41no—
162D4×C61—41no—
163D4×C61—41no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—81no—
173C2×C4×C61—81no—
174C2×C4×C61—81no—
175C2×C4×C61—81no—
176C2×C4×C61—81no—
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×Dic61—22no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—42no—
184C2×Dic61—42no—
185C2×Dic61—42no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—81no—
196C2×Dic61—81no—
197C2×Dic61—81no—
198C2×Dic61—81no—
199C2×Dic61—81no—
200C2×Dic61—81no—
201C2×Dic61#9911yescharacteristic
202C2×Dic61#9911yescharacteristic
203C8×C61—42no—
204#92418—42no—
205#13217—611nomaximal, Sylow
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61—41no—
216C22×C61—42no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61—41no—
220C22×C61—41no—
221C22×C61—81no—
222C22×C61#39011yescharacteristic
223C22×C61C2×#9911yescharacteristic
224C22×C61#41011yescharacteristic
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—81no—
228C4×C61—81no—
229C4×C61—161no—
230Dic61—21no—
231Dic61—41no—
232Dic61—41no—
233Dic61—41no—
234Dic61—81no—
235Dic61—81no—
236Dic61—161no—
237Dic61#35212yescomplemented
238#2486—611no—
239C2×#352—611no—
240C2×#352—611no—
241C2×#352—611no—
242C2×#352D6111yescharacteristic
243#1799—611no—
244C4×#100—611no—
245C2×C61—21no—
246C2×C61—21no—
247C2×C61—41no—
248C2×C61—41no—
249C2×C61—41no—
250C2×C61—41no—
251C2×C61#196411yescharacteristic
252C2×C61C2×#35211yescharacteristic
253C2×C61#212311yescharacteristic
254C2×#123—611no—
255C2×#123C2×D6111yescharacteristic
256C2×C4×D4—611no—
257C22×C4⋊C4—611no—
258C2×#100—611no—
259C2×#100C2×D6111yescharacteristic
260C2×#99—611no—
261C2×#99C2×D6111yescharacteristic
262C4×M16—1221no—
263#398—1221no—
264#397—1221no—
265#389—1221no—
266#381—611no—
267#381—611no—
268#380—611no—
269#380—1221no—
270#380—1221no—
271#352—22no—
272#352—1222no—
273#352—1222no—
274#352—1222no—
275#343—1221no—
276#342—1221no—
277C61#1321711yescharacteristic, complemented, Sylow
278C22×D4C22×D6111yescharacteristic
279C23×C4—611no—
280C23×C4—611no—
281C23×C4—611no—
282C23×C4C4×D6111yescharacteristic
283C2×M16—21no—
284C2×M16—1221no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—1221no—
290#123—1221no—
291#123—1221no—
292#123—1221no—
293C4×D4—2441no—
294C4×D4—2441no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—611no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4—1221no—
299C2×C4⋊C4—1221no—
300C2×C4⋊C4—1221no—
301C2×C4⋊C4—2441no—
302C2×C4⋊C4—2441no—
303C2×C4⋊C4—2441no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—611no—
307C2×C22⋊C4—611no—
308C2×C22⋊C4—611no—
309C2×C22⋊C4—1221no—
310C2×C22⋊C4—1221no—
311C2×C22⋊C4C4×D6111yescharacteristic
312C2×C42—611no—
313#100—21no—
314#100—612no—
315#100—1221no—
316#100C22⋊D6112yes—
317#99—21no—
318#99—21no—
319#99—1221no—
320#99—1221no—
321#97—2441no—
322C4×C8—2441no—
323#95—1221no—
324#95—1221no—
325#95—1221no—
326#95—1221no—
327#95—1221no—
328#95—2441no—
329C24C2×C4×D6111yescharacteristic
330C24D4×D6111yescharacteristic
331C2×D4—41no—
332C2×D4—41no—
333C2×D4#1175822211yescharacteristic
334C2×D4D4×D6111yescharacteristic
335C2×D4#1175822411yescharacteristic
336C2×D4C2×C22⋊D6111yescharacteristic
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4—1221no—
355C22×C4—1221no—
356C22×C4—2442no—
357C22×C4—2442no—
358C22×C4—2441no—
359C22×C4—2441no—
360C22×C4—2441no—
361C22×C4D4×D6111yescharacteristic
362M16—22no—
363M16—41no—
364M16—1222no—
365M16—2441no—
366C2×C8—41no—
367C2×C8—2441no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—4882no—
371C4⋊C4—2441no—
372C4⋊C4—2441no—
373C4⋊C4—2441no—
374C4⋊C4—2442no—
375C4⋊C4—2442no—
376C4⋊C4—2441no—
377C4⋊C4—2441no—
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—1221no—
385C22⋊C4—1221no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4—2441no—
391C22⋊C4—2441no—
392C42—1221no—
393C42—1221no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23C22⋊C4×D6111yescharacteristic
403C23#1451973711yescharacteristic
404C23C4×C22⋊D6111yescharacteristic
405C23#1451976311yescharacteristic
406C23#1451977311yescharacteristic
407D4—41no—
408D4—41no—
409D4—41no—
410D4—41no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—611no—
425C2×C4—611no—
426C2×C4—1222no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—4881no—
431C2×C4—4881no—
432C2×C4—4881no—
433C2×C4—4881no—
434C2×C4—4881no—
435C2×C4—4881no—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4#1451974911yescharacteristic
449C2×C4#1451975011yescharacteristic
450C8—42no—
451C8—2442no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—42no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—81no—
468C22#1683966211yescharacteristic
469C22#99×D6111yescharacteristic
470C22#1683973411yescharacteristic
471C4—21no—
472C4—21no—
473C4—81no—
474C4—81no—
475C4—161no—
476C4—612no—
477C4—1221no—
478C4—9761no—
479C4—4881no—
480C4—4881no—
481C4—2441no—
482C4—2441no—
483C4—2441no—
484C2—21no—
485C2—21no—
486C2—41no—
487C2—41no—
488C2—41no—
489C2—41no—
490C2#2144665311yescharacteristic
491C2#352×D6111yescharacteristic
492C2#2144747111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC24×C61C22×C4
FrattiniC22×D4C22×D61
FittingC2×C61×#352C2
socleC22×C61C2×#99
prime radical, cosocleC22×D4×C61C23
hypercenterC2×#352D61
hypocenterC61#13217
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

Complements

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

NH ≅ G/Ntype
10. C22×#11758196C4semidirect
17. #16839625C4semidirect
18. #16839623C4semidirect
21. #16839620C4semidirect
237. Dic61#352semidirect
277. C61#13217semidirect

Maximal subgroups

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

subgroupindex
#214501242
C2×#168395532
C2×#168395522
C2×#168395512
#214458052
#100×Dic612
C2×C61×#3522
#1321761