Finite Group Databasebeta

← C2×#21447815 #29834028

Subgroups — C2×#21447815 #29834028

Order 15616.

1244 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 171 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×#16839951C212yesmaximal, complemented
2C2×#16839929C211yesmaximal, characteristic
3#21447815C218yesmaximal, direct product factor
4C2×#16839555C211yesmaximal, characteristic, complemented
5C2×#16839552C212yesmaximal, complemented
6C2×C61×#559C211yesmaximal, characteristic, complemented
7C2×#14519822C2211yescharacteristic
8C2×#14519803—21no—
9C2×#14519760—22no—
10#16839951—24no—
11#16839951C2218yescomplemented
12#16839929—22no—
13#16839929C2214yes—
14C2×#14519705—21no—
15C2×#14519694C2211yescharacteristic
16C2×#14519692C2212yes—
17C2×#14519691—22no—
18#16839555C2214yescomplemented
19#16839552C2218yescomplemented
20C61×#559—22no—
21C61×#559—24no—
22C61×#559C2214yescomplemented
23C2×#127×C61C2211yescharacteristic
24C2×#124×C61—22no—
25C2×#123×C61—21no—
26C2×#123×C61C2212yes—
27C2×C4×Q8×C61—21no—
28C2×C4×D4×C61—22no—
29#14519822—21no—
30#14519822—22no—
31#14519822—42no—
32#14519822C2312yes—
33C2×#11758222—21no—
34C2×#11758224—41no—
35C22×C22⋊D61—22no—
36C2×D4×D61—41no—
37#14519803—24no—
38#14519803—42no—
39C2×#11758200—41no—
40C2×#11758199—41no—
41C2×#11758194—21no—
42#14519760—28no—
43#14519760—44no—
44C2×#11758196—42no—
45C2×C22⋊Dic61—22no—
46C2×#11758198—42no—
47#14519705—24no—
48#14519694—21no—
49#14519694C2312yes—
50#14519692—22no—
51#14519692C2314yes—
52#14519691—28no—
53C22×Q8×C61—21no—
54C22×D4×C61—22no—
55C22×D4×C61D411yescharacteristic
56C22×D4×C61C2311yescharacteristic
57C23×C4×C61—21no—
58C23×C4×C61D412yes—
59#127×C61—22no—
60#127×C61D412yes—
61#127×C61C2312yes—
62#124×C61—28no—
63#124×C61—28no—
64#123×C61—24no—
65#123×C61—22no—
66#123×C61—22no—
67#123×C61—24no—
68#123×C61D414yes—
69#123×C61C2314yes—
70C4×Q8×C61—24no—
71C4×Q8×C61—24no—
72C4×D4×C61—28no—
73C4×D4×C61—28no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61—22no—
76C2×C22⋊C4×C61—22no—
77C2×C22⋊C4×C61—21no—
78C2×C22⋊C4×C61—22no—
79C2×C22⋊C4×C61D412yes—
80C2×C42×C61—22no—
81C2×C42×C61D411yescharacteristic
82C24×C61—21no—
83C24×C61C2×D412yes—
84C23×D61—22no—
85C2×Q8×C61—24no—
86C2×Q8×C61—44no—
87C2×D4×C61—24no—
88C2×D4×C61—24no—
89C2×D4×C61—21no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—48no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61C2×D412yes—
96C2×D4×C61C2×D412yes—
97C2×D4×C61C2×D411yescharacteristic
98C2×D4×C61C2411yescharacteristic
99C22×C4×C61—21no—
100C22×C4×C61—22no—
101C22×C4×C61—22no—
102C22×C4×C61—24no—
103C22×C4×C61—22no—
104C22×C4×C61—42no—
105C22×C4×C61—42no—
106C22×C4×C61—81no—
107C22×C4×C61—81no—
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D414yes—
110C2×C22⋊D61—24no—
111C2×C22⋊D61—24no—
112C2×C22⋊D61—42no—
113C2×C22⋊D61—42no—
114C2×C22⋊D61—41no—
115C2×C22⋊D61—42no—
116C22×Dic61—22no—
117C22×Dic61—42no—
118#11758224—42no—
119#11758224—42no—
120#11758224—44no—
121D4×D61—42no—
122D4×D61—42no—
123D4×D61—44no—
124#11758222—22no—
125#11758222—22no—
126#11758222—41no—
127#11758222—41no—
128C2×D244—21no—
129C2×C4×D61—41no—
130C2×Dic122—21no—
131C4⋊C4×C61—24no—
132C4⋊C4×C61—24no—
133C4⋊C4×C61—24no—
134C22⋊C4×C61—28no—
135C22⋊C4×C61—24no—
136C22⋊C4×C61—24no—
137C22⋊C4×C61—22no—
138C22⋊C4×C61—24no—
139C22⋊C4×C61C2×D414yes—
140C42×C61—28no—
141C42×C61—21no—
142C42×C61C2×D412yes—
143C22⋊Dic61—24no—
144C22⋊Dic61—42no—
145#11758200—44no—
146#11758199—44no—
147#11758198—48no—
148#11758196—48no—
149#11758194—22no—
150#11758194—41no—
151C2×#92418—41no—
152C23×C61—22no—
153C23×C61—22no—
154C23×C61—22no—
155C23×C61—44no—
156C23×C61—44no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61#12011yescharacteristic
160C23×C61#12012yes—
161C23×C61C22×D412yes—
162C22×D61—24no—
163C22×D61—41no—
164C22×D61—42no—
165C22×D61—84no—
166Q8×C61—48no—
167D4×C61—41no—
168D4×C61—42no—
169D4×C61—41no—
170D4×C61—42no—
171D4×C61—48no—
172D4×C61—48no—
173D4×C61—81no—
174C2×C4×C61—24no—
175C2×C4×C61—22no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—24no—
179C2×C4×C61—24no—
180C2×C4×C61—44no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—44no—
184C2×C4×C61—82no—
185C2×C4×C61—84no—
186C2×C4×C61#12011yescharacteristic
187C2×C4×C61C22×D411yescharacteristic
188C22⋊D61—44no—
189C22⋊D61—44no—
190C22⋊D61—42no—
191C22⋊D61—42no—
192C2×Dic61—24no—
193C2×Dic61—42no—
194C2×Dic61—41no—
195C2×Dic61—44no—
196C2×Dic61—84no—
197D244—22no—
198D244—41no—
199C4×D61—42no—
200C4×D61—42no—
201Dic122—22no—
202Dic122—41no—
203#92418—42no—
204C2×#2198—611nomaximal, Sylow
205C22×C61—22no—
206C22×C61—22no—
207C22×C61—22no—
208C22×C61—42no—
209C22×C61—42no—
210C22×C61—44no—
211C22×C61—44no—
212C22×C61—42no—
213C22×C61—82no—
214C22×C61—82no—
215C22×C61—82no—
216C22×C61B(4,𝔽2)11yescharacteristic
217C22×C61B(4,𝔽2)11yescharacteristic
218C22×C61C2×#12011yescharacteristic
219C2×D61—42no—
220C2×D61—82no—
221C2×D61—84no—
222C2×D61—162no—
223C4×C61—24no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—44no—
227C4×C61—44no—
228Dic61—42no—
229Dic61—84no—
230C2×#559D6111yescharacteristic, complemented
231C2×#458—612no—
232C2×#453—611no—
233#2198—618no—
234C2×#353—611no—
235C2×#352—612no—
236C2×C61—21no—
237C2×C61—21no—
238C2×C61—42no—
239C2×C61—42no—
240C2×C61—82no—
241C2×C61#219812yescomplemented
242C2×C61C2×B(4,𝔽2)11yescharacteristic
243D61—82no—
244C2×H(5,𝔽2)—611no—
245C2×AGL(1,ℤ/8)—1221no—
246#559—22no—
247#559—24no—
248#559C2×D6114yescomplemented
249C2×#127C2×D6111yescharacteristic
250C2×#124—22no—
251C2×#123—21no—
252C2×#123—1222no—
253C2×#123C2×D6112yes—
254C2×C4×Q8—21no—
255C2×C4×D4—22no—
256#458—618no—
257#458—1224no—
258#453—614no—
259#453—1222no—
260C2×#104—1221no—
261C2×#100—611no—
262C2×#99—612no—
263C2×#99—1222no—
264#353—614no—
265#352—618no—
266C61C2×#219811yescharacteristic, complemented, Sylow
267H(5,𝔽2)—612no—
268H(5,𝔽2)—1222no—
269H(5,𝔽2)—1221no—
270H(5,𝔽2)—2442no—
271C2×#41—1221no—
272C2×#41—2441no—
273C22×Q8—21no—
274C22×D4—22no—
275C22×D4—1222no—
276C22×D4—2441no—
277C22×D4C22⋊D6111yescharacteristic
278C22×D4C22×D6111yescharacteristic
279C23×C4—21no—
280C23×C4C22⋊D6112yes—
281AGL(1,ℤ/8)—1224no—
282AGL(1,ℤ/8)—2442no—
283C2×SD16—2441no—
284C2×D8—2441no—
285C2×M16—1221no—
286#127—22no—
287#127C22⋊D6112yes—
288#127C22×D6112yes—
289#124—28no—
290#124—28no—
291#123—24no—
292#123—24no—
293#123—22no—
294#123—22no—
295#123—1228no—
296#123—2444no—
297#123C22⋊D6114yes—
298#123C22×D6114yes—
299C4×Q8—24no—
300C4×Q8—24no—
301C4×D4—28no—
302C4×D4—28no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—2442no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—1222no—
310C2×C22⋊C4—2442no—
311C2×C22⋊C4C22⋊D6112yes—
312C2×C42—22no—
313C2×C42C22⋊D6111yescharacteristic
314#104—1224no—
315#100—612no—
316#100—1221no—
317#99—614no—
318#99—1222no—
319#99—1228no—
320C24—21no—
321C24—1222no—
322C24C2×C22⋊D6112yes—
323#41—1222no—
324#41—1222no—
325#41—2441no—
326#41—2442no—
327#41—2444no—
328#41—2442no—
329#41—2441no—
330C2×Q8—24no—
331C2×Q8—44no—
332C2×Q8—1221no—
333C2×D4—24no—
334C2×D4—24no—
335C2×D4—21no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—48no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—1221no—
342C2×D4—1224no—
343C2×D4—1224no—
344C2×D4—2442no—
345C2×D4—2442no—
346C2×D4—2444no—
347C2×D4—2442no—
348C2×D4—2442no—
349C2×D4—2442no—
350C2×D4—2441no—
351C2×D4C2×C22⋊D6112yes—
352C2×D4C2×C22⋊D6111yescharacteristic
353C2×D4C2×C22⋊D6112yes—
354C2×D4C23×D6111yescharacteristic
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—81no—
363C22×C4—81no—
364C22×C4—1222no—
365C22×C4—2441no—
366C22×C4—2442no—
367C22×C4C2×C22⋊D6111yescharacteristic
368C22×C4C2×C22⋊D6114yes—
369SD16—2444no—
370D8—2444no—
371M16—1222no—
372M16—2441no—
373C2×C8—2441no—
374C4⋊C4—24no—
375C4⋊C4—24no—
376C4⋊C4—24no—
377C4⋊C4—2448no—
378C22⋊C4—28no—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—24no—
382C22⋊C4—22no—
383C22⋊C4—1224no—
384C22⋊C4—2448no—
385C22⋊C4—2442no—
386C22⋊C4C2×C22⋊D6114yes—
387C42—28no—
388C42—21no—
389C42C2×C22⋊D6112yes—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—44no—
394C23—44no—
395C23—41no—
396C23—41no—
397C23—1224no—
398C23—4884no—
399C23—2442no—
400C23—2441no—
401C23#1451974612yes—
402C23#1451974611yescharacteristic
403C23C22×C22⋊D6112yes—
404Q8—48no—
405Q8—1222no—
406Q8—2441no—
407D4—41no—
408D4—42no—
409D4—41no—
410D4—42no—
411D4—48no—
412D4—48no—
413D4—81no—
414D4—1222no—
415D4—2441no—
416D4—2444no—
417D4—2444no—
418D4—2442no—
419D4—2442no—
420C2×C4—24no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—44no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—82no—
431C2×C4—84no—
432C2×C4—1224no—
433C2×C4—4884no—
434C2×C4—2442no—
435C2×C4—2442no—
436C2×C4—2444no—
437C2×C4—2442no—
438C2×C4—2441no—
439C2×C4#1451974611yescharacteristic
440C2×C4C22×C22⋊D6111yescharacteristic
441C8—2442no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—42no—
446C22—42no—
447C22—44no—
448C22—44no—
449C22—42no—
450C22—82no—
451C22—82no—
452C22—82no—
453C22—9762no—
454C22—4884no—
455C22—4882no—
456C22—2442no—
457C22#1683994911yescharacteristic
458C22#1683994911yescharacteristic
459C22C2×#1451974611yescharacteristic
460C4—24no—
461C4—21no—
462C4—21no—
463C4—44no—
464C4—44no—
465C4—4884no—
466C4—2442no—
467C2—21no—
468C2—21no—
469C2—42no—
470C2—42no—
471C2—82no—
472C2—4882no—
473C2#2144781512yesdirect product factor
474C2C2×#1683994911yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×D4×C61C24
FrattiniC2×D4C23×D61
FittingC2×C61×#559C2
socleC22×C61B(4,𝔽2)
prime radicalC2×#16839929C2
hypercenterC2×#559D61
hypocenterC61C2×#2198
LCSG ▷ C2×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#16839951C2semidirect
3. #21447815C2direct (N × H)
4. C2×#16839555C2semidirect
5. C2×#16839552C2semidirect
6. C2×C61×#559C2semidirect
11. #16839951C22semidirect
18. #16839555C22semidirect
19. #16839552C22semidirect
22. C61×#559C22semidirect
230. C2×#559D61semidirect
241. C2×C61#2198semidirect
248. #559C2×D61semidirect
266. C61C2×#2198semidirect
473. C2#21447815direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168399512
C2×#168399292
#214478152
C2×#168395552
C2×#168395522
C2×C61×#5592
C2×#219861