Finite Group Databasebeta

← C2×#21447840 #29834171

Subgroups — C2×#21447840 #29834171

Order 15616.

1092 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1092 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×#16839944C212yesmaximal, complemented
2C2×#16839934C211yesmaximal, characteristic
3#21447840C218yesmaximal, direct product factor
4C2×#16839561C212yesmaximal, complemented
5C2×#16839559C211yesmaximal, characteristic, complemented
6C2×C61×#563C211yesmaximal, characteristic, complemented
7C2×#14519825C2211yescharacteristic
8C2×#14519808—22no—
9C2×#14519803—21no—
10#16839944—24no—
11#16839944C2218yescomplemented
12#16839934—22no—
13#16839934C2214yes—
14C2×#14519705—21no—
15C2×#14519705—22no—
16C2×#14519696C2211yescharacteristic
17C2×#14519696C2212yes—
18#16839561C2218yescomplemented
19#16839559C2214yescomplemented
20C61×#563—24no—
21C61×#563—22no—
22C61×#563C2214yescomplemented
23C2×C4⋊Q8×C61C2212yes—
24C2×#126×C61—22no—
25C2×#125×C61—21no—
26C2×#124×C61C2211yescharacteristic
27C2×#123×C61—21no—
28C2×C22⋊Q8×C61—22no—
29#14519825—22no—
30#14519825—21no—
31#14519825—42no—
32#14519825C2312yes—
33C2×#11758226—41no—
34C2×#11758222—21no—
35C2×#11758222—22no—
36C2×Q8×D61—41no—
37#14519808—28no—
38#14519808—44no—
39#14519803—24no—
40#14519803—42no—
41C2×#11758202—42no—
42C2×#11758200—41no—
43C2×#11758201—42no—
44C2×#11758199—41no—
45C2×#11758194—21no—
46C2×#11758194—22no—
47#14519705—28no—
48#14519705—24no—
49#14519696—22no—
50#14519696—21no—
51#14519696C2314yes—
52#14519696C2312yes—
53C22×Q8×C61D412yes—
54C22×Q8×C61C2311yescharacteristic
55C22×D4×C61D411yescharacteristic
56C23×C4×C61—21no—
57C4⋊Q8×C61—22no—
58C4⋊Q8×C61—22no—
59C4⋊Q8×C61D414yes—
60C4⋊Q8×C61C2314yes—
61#126×C61—28no—
62#126×C61—28no—
63#125×C61—24no—
64#125×C61—24no—
65#124×C61—22no—
66#124×C61D412yes—
67#124×C61C2312yes—
68#123×C61—24no—
69#123×C61—24no—
70C22⋊Q8×C61—28no—
71C22⋊Q8×C61—28no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—22no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61—22no—
76C2×C4⋊C4×C61—22no—
77C2×C22⋊C4×C61—22no—
78C2×C22⋊C4×C61—21no—
79C2×C22⋊C4×C61—22no—
80C2×C42×C61D412yes—
81C2×C42×C61D411yescharacteristic
82C24×C61—21no—
83C2×Q8×C61—22no—
84C2×Q8×C61—41no—
85C2×Q8×C61—41no—
86C2×Q8×C61—42no—
87C2×Q8×C61—42no—
88C2×Q8×C61C2×D414yes—
89C2×Q8×C61C2×D412yes—
90C2×Q8×C61C2×D411yescharacteristic
91C2×Q8×C61C2411yescharacteristic
92C2×D4×C61—21no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61C2×D412yes—
96C22×C4×C61—22no—
97C22×C4×C61—21no—
98C22×C4×C61—22no—
99C22×C4×C61—24no—
100C22×C4×C61—81no—
101C22×C4×C61—81no—
102C22×C4×C61C2×D412yes—
103C22×C4×C61C2×D411yescharacteristic
104C2×C22⋊D61—41no—
105#11758226—42no—
106#11758226—42no—
107#11758226—44no—
108Q8×D61—42no—
109Q8×D61—42no—
110Q8×D61—44no—
111#11758222—24no—
112#11758222—22no—
113#11758222—24no—
114#11758222—22no—
115#11758222—41no—
116#11758222—42no—
117#11758222—42no—
118#11758222—41no—
119C2×D244—21no—
120C2×D244—22no—
121C2×C4×D61—41no—
122C2×C4×D61—42no—
123C2×Dic122—21no—
124C2×Dic122—22no—
125C4⋊C4×C61—24no—
126C4⋊C4×C61—28no—
127C4⋊C4×C61—24no—
128C4⋊C4×C61—24no—
129C4⋊C4×C61—24no—
130C4⋊C4×C61—24no—
131C4⋊C4×C61—24no—
132C22⋊C4×C61—28no—
133C22⋊C4×C61—24no—
134C22⋊C4×C61—24no—
135C22⋊C4×C61—24no—
136C42×C61—21no—
137C42×C61—22no—
138C42×C61C2×D412yes—
139C42×C61C2×D414yes—
140#11758202—48no—
141#11758201—48no—
142#11758200—44no—
143#11758199—44no—
144#11758194—24no—
145#11758194—22no—
146#11758194—42no—
147#11758194—41no—
148C2×#92418—41no—
149C2×#92418—42no—
150C23×C61—22no—
151C23×C61—44no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61#12011yescharacteristic
155C22×D61—41no—
156Q8×C61—41no—
157Q8×C61—42no—
158Q8×C61—41no—
159Q8×C61—44no—
160Q8×C61—82no—
161D4×C61—42no—
162D4×C61—81no—
163C2×C4×C61—21no—
164C2×C4×C61—22no—
165C2×C4×C61—21no—
166C2×C4×C61—22no—
167C2×C4×C61—22no—
168C2×C4×C61—24no—
169C2×C4×C61—24no—
170C2×C4×C61—44no—
171C2×C4×C61—42no—
172C2×C4×C61—42no—
173C2×C4×C61—42no—
174C2×C4×C61—84no—
175C2×C4×C61#12012yes—
176C2×C4×C61#12011yescharacteristic
177C2×C4×C61C22×D412yes—
178C2×C4×C61C22×D411yescharacteristic
179C22⋊D61—42no—
180C22⋊D61—42no—
181C2×Dic61—41no—
182D244—22no—
183D244—24no—
184D244—41no—
185D244—42no—
186C4×D61—42no—
187C4×D61—44no—
188C4×D61—42no—
189C4×D61—44no—
190Dic122—22no—
191Dic122—24no—
192Dic122—41no—
193Dic122—42no—
194#92418—42no—
195#92418—44no—
196C2×#2203—611nomaximal, Sylow
197C22×C61—22no—
198C22×C61—44no—
199C22×C61—42no—
200C22×C61—82no—
201C22×C61—82no—
202C22×C61B(4,𝔽2)11yescharacteristic
203C22×C61B(4,𝔽2)11yescharacteristic
204C22×C61C2×#12011yescharacteristic
205C2×D61—42no—
206C2×D61—82no—
207C4×C61—21no—
208C4×C61—22no—
209C4×C61—21no—
210C4×C61—22no—
211C4×C61—42no—
212C4×C61—44no—
213C4×C61—44no—
214Dic61—42no—
215C2×#563D6111yescharacteristic, complemented
216C2×#456—612no—
217C2×#454—611no—
218#2203—618no—
219C2×#356—612no—
220C2×#355—611no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61—82no—
224C2×C61#220312yescomplemented
225C2×C61C2×B(4,𝔽2)11yescharacteristic
226D61—82no—
227C2×2−1+4—611no—
228C2×#137—1222no—
229C2×AGL(1,ℤ/8)—1221no—
230#563—24no—
231#563—22no—
232#563C2×D6114yescomplemented
233C2×C4⋊Q8C2×D6112yes—
234C2×#126—22no—
235C2×#125—21no—
236C2×#124C2×D6111yescharacteristic
237C2×#123—21no—
238C2×C22⋊Q8—22no—
239#456—618no—
240#456—1224no—
241#454—614no—
242#454—1222no—
243C2×#104—1221no—
244C2×#104—1222no—
245C2×#101—612no—
246C2×#101—611no—
247#356—618no—
248#355—614no—
249C61C2×#220311yescharacteristic, complemented, Sylow
2502−1+4—612no—
2512−1+4—1221no—
2522−1+4—1222no—
2532−1+4—2442no—
254C2×#41—1221no—
255C2×#41—1222no—
256C2×#41—2441no—
257C22×Q8—2441no—
258C22×Q8C22⋊D6112yes—
259C22×Q8C22×D6111yescharacteristic
260C22×D4C22⋊D6111yescharacteristic
261C23×C4—21no—
262#137—1228no—
263#137—2444no—
264AGL(1,ℤ/8)—1224no—
265AGL(1,ℤ/8)—2442no—
266C2×Q16—2442no—
267C2×SD16—2441no—
268C2×SD16—2442no—
269C2×D8—2441no—
270C2×M16—1221no—
271C2×M16—1222no—
272C4⋊Q8—22no—
273C4⋊Q8—22no—
274C4⋊Q8C22⋊D6114yes—
275C4⋊Q8C22×D6114yes—
276#126—28no—
277#126—28no—
278#125—24no—
279#125—24no—
280#124—22no—
281#124C22⋊D6112yes—
282#124C22×D6112yes—
283#123—24no—
284#123—24no—
285C22⋊Q8—28no—
286C22⋊Q8—28no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C42C22⋊D6111yescharacteristic
296C2×C42C22⋊D6112yes—
297#104—1224no—
298#104—1228no—
299#101—614no—
300#101—612no—
301#101—1221no—
302#101—1222no—
303C24—21no—
304#41—1222no—
305#41—1224no—
306#41—1222no—
307#41—1224no—
308#41—2441no—
309#41—2442no—
310#41—2442no—
311#41—2442no—
312#41—2444no—
313#41—2442no—
314#41—2441no—
315C2×Q8—22no—
316C2×Q8—41no—
317C2×Q8—41no—
318C2×Q8—42no—
319C2×Q8—42no—
320C2×Q8—1221no—
321C2×Q8—1222no—
322C2×Q8—2442no—
323C2×Q8—2442no—
324C2×Q8—2444no—
325C2×Q8C2×C22⋊D6114yes—
326C2×Q8C2×C22⋊D6112yes—
327C2×Q8C2×C22⋊D6111yescharacteristic
328C2×Q8C23×D6111yescharacteristic
329C2×D4—21no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—1221no—
333C2×D4—1222no—
334C2×D4—2441no—
335C2×D4C2×C22⋊D6112yes—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—81no—
341C22×C4—81no—
342C22×C4—2441no—
343C22×C4—2442no—
344C22×C4C2×C22⋊D6112yes—
345C22×C4C2×C22⋊D6111yescharacteristic
346Q16—2448no—
347SD16—2444no—
348SD16—2448no—
349D8—2444no—
350M16—1222no—
351M16—1224no—
352M16—2441no—
353M16—2442no—
354C2×C8—2441no—
355C2×C8—2442no—
356C4⋊C4—24no—
357C4⋊C4—28no—
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C22⋊C4—28no—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—24no—
367C42—21no—
368C42—22no—
369C42C2×C22⋊D6112yes—
370C42C2×C22⋊D6114yes—
371C23—22no—
372C23—44no—
373C23—41no—
374C23—41no—
375C23—2441no—
376C23#1451974611yescharacteristic
377Q8—41no—
378Q8—42no—
379Q8—41no—
380Q8—44no—
381Q8—82no—
382Q8—1222no—
383Q8—1224no—
384Q8—2441no—
385Q8—2442no—
386D4—42no—
387D4—81no—
388D4—1222no—
389D4—1224no—
390D4—2441no—
391D4—2442no—
392D4—2442no—
393D4—2442no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—84no—
406C2×C4—2442no—
407C2×C4—2444no—
408C2×C4—2442no—
409C2×C4—2444no—
410C2×C4—2441no—
411C2×C4#1451974612yes—
412C2×C4#1451974611yescharacteristic
413C2×C4C22×C22⋊D6112yes—
414C2×C4C22×C22⋊D6111yescharacteristic
415C8—2442no—
416C8—2444no—
417C22—22no—
418C22—44no—
419C22—42no—
420C22—82no—
421C22—82no—
422C22—4882no—
423C22—2442no—
424C22#1683994911yescharacteristic
425C22#1683994911yescharacteristic
426C22C2×#1451974611yescharacteristic
427C4—21no—
428C4—22no—
429C4—21no—
430C4—22no—
431C4—42no—
432C4—44no—
433C4—44no—
434C4—2442no—
435C2—21no—
436C2—21no—
437C2—82no—
438C2—4882no—
439C2#2144784012yesdirect product factor
440C2C2×#1683994911yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×Q8×C61C24
FrattiniC2×Q8C23×D61
FittingC2×C61×#563C2
socleC22×C61B(4,𝔽2)
prime radicalC2×#16839934C2
hypercenterC2×#563D61
hypocenterC61C2×#2203
LCSG ▷ C2×Q8×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#563

Complements

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

NH ≅ G/Ntype
1. C2×#16839944C2semidirect
3. #21447840C2direct (N × H)
4. C2×#16839561C2semidirect
5. C2×#16839559C2semidirect
6. C2×C61×#563C2semidirect
11. #16839944C22semidirect
18. #16839561C22semidirect
19. #16839559C22semidirect
22. C61×#563C22semidirect
215. C2×#563D61semidirect
224. C2×C61#2203semidirect
232. #563C2×D61semidirect
249. C61C2×#2203semidirect
439. C2#21447840direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168399442
C2×#168399342
#214478402
C2×#168395612
C2×#168395592
C2×C61×#5632
C2×#220361