Finite Group Databasebeta

← C2×#19133537 #25068777

Subgroups — C2×#19133537 #25068777

Order 11008.

1372 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1372 conjugacy classes of subgroups — too many to draw. Only its 203 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×#14583530C211yesmaximal, characteristic, complemented
2C2×#14583052C212yesmaximal
3C2×#14582816C211yesmaximal, characteristic
4#19133537C218yesmaximal, direct product factor
5C2×#14582637C212yesmaximal, complemented
6C2×C43×#324C211yesmaximal, characteristic, complemented
7C23×D172C2211yescharacteristic
8C22×#10621873—22no—
9#14583530—24no—
10#14583530—22no—
11#14583530C2214yescomplemented
12C2×#13063324—22no—
13C2×#13063316—22no—
14C2×#13063304—21no—
15C2×#13063304C2212yes—
16C2×#13063284—21no—
17C22×(C2×D43)⋊C4—21no—
18C22×(C2×D43)⋊C4—21no—
19#14583052—24no—
20#14583052C2218yes—
21C2×#13063247—22no—
22#14582816—22no—
23#14582816C2214yes—
24C2×C43⋊#95C2211yescharacteristic
25#14582637C2218yescomplemented
26C22×C4⋊C4×C43C2211yescharacteristic
27C2×C22⋊C8×C43C2212yes—
28C43×#324C2214yescomplemented
29C24×D43—21no—
30C22×Dic86—21no—
31C22×Dic86D412yes—
32C22×D172—22no—
33C22×D172—22no—
34C22×D172—21no—
35C22×D172—44no—
36C22×D172C2312yes—
37C23×Dic43—21no—
38C2×#10621873—28no—
39C2×#10621873—48no—
40#13063324—28no—
41#13063324—28no—
42#13063316—28no—
43#13063316—28no—
44#13063304—24no—
45#13063304—24no—
46#13063304—22no—
47#13063304—22no—
48#13063304D414yes—
49#13063304C2314yes—
50#13063284—24no—
51#13063284—24no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43D412yes—
56C2×Dic43⋊C4—22no—
57C2×Dic43⋊C4—22no—
58C2×C22⋊Dic43—22no—
59C2×(C2×D43)⋊C4—24no—
60C2×(C2×D43)⋊C4—24no—
61C2×(C2×D43)⋊C4—44no—
62C2×(C2×D43)⋊C4—44no—
63C2×C4×Dic43—22no—
64#13063247—28no—
65C43⋊#95—21no—
66C43⋊#95C2312yes—
67C23×C4×C43D411yescharacteristic
68C23×C4×C43D411yescharacteristic
69C23×C4×C43C2311yescharacteristic
70C22×C8×C43—22no—
71C2×C4⋊C4×C43—22no—
72C2×C4⋊C4×C43—22no—
73C2×C4⋊C4×C43D412yes—
74C2×C4⋊C4×C43C2312yes—
75C22⋊C8×C43—22no—
76C22⋊C8×C43C2314yes—
77C24×C43C2×D411yescharacteristic
78C23×D43—24no—
79C23×D43—22no—
80C23×D43—42no—
81C23×D43—42no—
82C23×D43—42no—
83C23×D43—41no—
84C23×D43—41no—
85C23×D43—42no—
86C23×D43—42no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—22no—
92C22×C4×C43—42no—
93C22×C4×C43—42no—
94C22×C4×C43SD1614yescomplemented
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2×D412yes—
97C22×C4×C43C2×D412yes—
98C22×C4×C43C2×D412yes—
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2411yescharacteristic
101C22×Dic43—22no—
102C22×Dic43—22no—
103C22×Dic43—22no—
104C22×Dic43—42no—
105C22×Dic43—42no—
106C22×Dic43—42no—
107C2×D172—28no—
108C2×D172—24no—
109C2×D172—44no—
110C2×D172—44no—
111C2×D172—48no—
112C2×D172—44no—
113C2×D172—42no—
114C2×Dic86—24no—
115C2×Dic86—22no—
116C2×Dic86—44no—
117C2×Dic86—82no—
118C2×Dic86C2×D414yes—
119C2×C8×C43—24no—
120C2×C8×C43—44no—
121C4⋊C4×C43—24no—
122C4⋊C4×C43—24no—
123C22⋊Dic43—24no—
124C22⋊Dic43—24no—
125(C2×D43)⋊C4—48no—
126(C2×D43)⋊C4—48no—
127C4⋊Dic43—24no—
128C4⋊Dic43—24no—
129C4⋊Dic43—24no—
130C4⋊Dic43—22no—
131C4⋊Dic43C2×D414yes—
132Dic43⋊C4—28no—
133Dic43⋊C4—24no—
134Dic43⋊C4—24no—
135C4×Dic43—28no—
136#10621873—416no—
137C23×C43—22no—
138C23×C43—22no—
139C23×C43#12011yescharacteristic
140C23×C43#12011yescharacteristic
141C23×C43C2×SD1612yes—
142C23×C43#13712yes—
143C23×C43C22×D411yescharacteristic
144C22×D43—24no—
145C22×D43—42no—
146C22×D43—44no—
147C22×D43—48no—
148C22×D43—48no—
149C22×D43—42no—
150C22×D43—42no—
151C22×D43—42no—
152C22×D43—42no—
153C22×D43—42no—
154C22×D43—44no—
155C22×D43—84no—
156C22×D43—84no—
157C22×D43—82no—
158C22×D43—82no—
159C22×D43—82no—
160C22×D43—82no—
161C2×C4×C43—22no—
162C2×C4×C43—22no—
163C2×C4×C43—24no—
164C2×C4×C43—24no—
165C2×C4×C43—24no—
166C2×C4×C43—22no—
167C2×C4×C43—41no—
168C2×C4×C43—42no—
169C2×C4×C43—41no—
170C2×C4×C43—42no—
171C2×C4×C43—42no—
172C2×C4×C43—81no—
173C2×C4×C43#12012yes—
174C2×C4×C43C2×SD1614yescomplemented
175C2×C4×C43C22×D412yes—
176C2×Dic43—24no—
177C2×Dic43—24no—
178C2×Dic43—44no—
179C2×Dic43—44no—
180C2×Dic43—42no—
181C2×Dic43—42no—
182C2×Dic43—42no—
183C2×Dic43—84no—
184D172—28no—
185D172—44no—
186D172—48no—
187Dic86—44no—
188Dic86—82no—
189Dic86—84no—
190C8×C43—44no—
191C2×#1599—431nomaximal, Sylow
192C22×C43—24no—
193C22×C43—24no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43#44812yes—
199C22×C43#44812yes—
200C22×C43#45412yes—
201C22×C43B(4,𝔽2)12yes—
202C22×C43C2×#12011yescharacteristic
203C22×C43C22×SD1611yescharacteristic
204C22×C43C2×#13711yescharacteristic
205C2×D43—44no—
206C2×D43—44no—
207C2×D43—44no—
208C2×D43—82no—
209C2×D43—82no—
210C2×D43—88no—
211C2×D43—88no—
212C2×D43—82no—
213C2×D43—82no—
214C4×C43—24no—
215C4×C43—22no—
216C4×C43—22no—
217C4×C43—42no—
218Dic43—44no—
219Dic43—44no—
220Dic43—82no—
221C2×#544—431no—
222C2×#450—432no—
223C2×#394—431no—
224#1599—438no—
225C2×#328—432no—
226C2×#324D4311yescharacteristic, complemented
227C2×C43—21no—
228C2×C43—21no—
229C2×C43—22no—
230C2×C43#159914yescomplemented
231C2×C43C2×#44811yescharacteristic
232C2×C43C2×#45411yescharacteristic
233C2×C43C2×B(4,𝔽2)11yescharacteristic
234D43—84no—
235C23×D4—431no—
236C22×SD16—862no—
237#544—434no—
238#544—864no—
239#544—862no—
240C2×C4⋊Q8—862no—
241C2×#125—862no—
242C2×C22⋊Q8—432no—
243C2×C22⋊Q8—861no—
244C2×#117—861no—
245C22×C4⋊C4C2×D4311yescharacteristic
246C22×C22⋊C4—861no—
247C22×C22⋊C4—861no—
248#450—438no—
249#450—864no—
250C2×#102—862no—
251C2×C22⋊C8C2×D4312yes—
252#394—434no—
253#394—862no—
254C2×#95—431no—
255#328—438no—
256#324C2×D4314yescomplemented
257C43C2×#159911yescharacteristic, complemented, Sylow
258C25—861no—
259C22×Q8—432no—
260C22×Q8—861no—
261C22×D4—432no—
262C22×D4—861no—
263C22×D4—862no—
264C22×D4—862no—
265C22×D4—1724no—
266C23×C4—861no—
267C23×C4D17211yescharacteristic
268C23×C4D17211yescharacteristic
269C23×C4C22×D4311yescharacteristic
270C2×SD16—868no—
271C2×SD16—1728no—
272C22×C8—22no—
273C4⋊Q8—868no—
274C4⋊Q8—868no—
275#125—868no—
276#125—868no—
277C22⋊Q8—434no—
278C22⋊Q8—434no—
279C22⋊Q8—864no—
280C22⋊Q8—862no—
281C22⋊Q8—864no—
282C22⋊Q8—862no—
283#117—864no—
284#117—864no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—432no—
288C2×C4⋊C4—861no—
289C2×C4⋊C4—861no—
290C2×C4⋊C4—861no—
291C2×C4⋊C4—862no—
292C2×C4⋊C4—862no—
293C2×C4⋊C4D17212yes—
294C2×C4⋊C4C22×D4312yes—
295C2×C22⋊C4—862no—
296C2×C22⋊C4—864no—
297C2×C22⋊C4—864no—
298C2×C22⋊C4—1724no—
299C2×C22⋊C4—1724no—
300C2×C42—862no—
301#102—868no—
302C22⋊C8—22no—
303C22⋊C8C22×D4314yes—
304#95—432no—
305#95—861no—
306C24—864no—
307C24—862no—
308C24—1722no—
309C24—1722no—
310C24—1722no—
311C24—1721no—
312C24—1721no—
313C24—1722no—
314C24—1722no—
315C24C2×D17211yescharacteristic
316C2×Q8—434no—
317C2×Q8—864no—
318C2×Q8—862no—
319C2×Q8—3442no—
320C2×Q8—1724no—
321C2×D4—868no—
322C2×D4—864no—
323C2×D4—1724no—
324C2×D4—1724no—
325C2×D4—1728no—
326C2×D4—1724no—
327C2×D4—1722no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—862no—
336C22×C4—862no—
337C22×C4—862no—
338C22×C4—1722no—
339C22×C4—1722no—
340C22×C4—1722no—
341C22×C4#1062187314yescomplemented
342C22×C4C2×D17212yes—
343C22×C4C2×D17212yes—
344C22×C4C2×D17211yescharacteristic
345C22×C4D4×D4312yes—
346C22×C4D4×D4312yes—
347C22×C4C23×D4311yescharacteristic
348SD16—17216no—
349C2×C8—24no—
350C2×C8—44no—
351C4⋊C4—24no—
352C4⋊C4—24no—
353C4⋊C4—434no—
354C4⋊C4—864no—
355C4⋊C4—864no—
356C4⋊C4—864no—
357C4⋊C4—868no—
358C4⋊C4—862no—
359C4⋊C4—864no—
360C4⋊C4—864no—
361C22⋊C4—864no—
362C22⋊C4—864no—
363C22⋊C4—1728no—
364C22⋊C4—1728no—
365C42—868no—
366C23—22no—
367C23—22no—
368C23—864no—
369C23—3444no—
370C23—3444no—
371C23—3442no—
372C23—3442no—
373C23—3442no—
374C23—3442no—
375C23—1722no—
376C23—1724no—
377C23—1728no—
378C23—1728no—
379C23—1722no—
380C23—1722no—
381C23—1724no—
382C23—1722no—
383C23—1722no—
384C23—1722no—
385C23#1306329511yescharacteristic
386C23#1306329511yescharacteristic
387C23C2×#1062187312yes—
388C23#1306335812yes—
389C23C22×D17211yescharacteristic
390Q8—3442no—
391Q8—3444no—
392Q8—1724no—
393D4—868no—
394D4—1724no—
395D4—1728no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—81no—
408C2×C4—864no—
409C2×C4—864no—
410C2×C4—3444no—
411C2×C4—1722no—
412C2×C4—1722no—
413C2×C4—1722no—
414C2×C4—1724no—
415C2×C4—1724no—
416C2×C4#1306329512yes—
417C2×C4C2×#1062187314yescomplemented
418C2×C4C2×D4×D4312yes—
419C8—44no—
420C22—21no—
421C22—21no—
422C22—24no—
423C22—24no—
424C22—21no—
425C22—21no—
426C22—3442no—
427C22—3448no—
428C22—3442no—
429C22—3448no—
430C22—3442no—
431C22—3442no—
432C22—1724no—
433C22—1724no—
434C22—1724no—
435C22#1458304012yes—
436C22#1458304012yes—
437C22#1458307412yes—
438C22#1458308712yes—
439C22C2×#1306329511yescharacteristic
440C22C22×#1062187311yescharacteristic
441C22C2×#1306335811yescharacteristic
442C4—22no—
443C4—22no—
444C4—24no—
445C4—42no—
446C4—3442no—
447C4—1724no—
448C4—1724no—
449C2—21no—
450C2—22no—
451C2—21no—
452C2—3444no—
453C2#1913353714yesdirect product factor
454C2C2×#1458304011yescharacteristic
455C2C2×#1458307411yescharacteristic
456C2C2×#1458308711yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#324C2
socleC23×C43#120
prime radicalC23×D172C22
hypercenterC2×#324D43
hypocenterC43C2×#1599
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
1. C2×#14583530C2semidirect
4. #19133537C2direct (N × H)
5. C2×#14582637C2semidirect
6. C2×C43×#324C2semidirect
11. #14583530C22semidirect
25. #14582637C22semidirect
28. C43×#324C22semidirect
94. C22×C4×C43SD16semidirect
174. C2×C4×C43C2×SD16semidirect
226. C2×#324D43semidirect
230. C2×C43#1599semidirect
256. #324C2×D43semidirect
257. C43C2×#1599semidirect
341. C22×C4#10621873semidirect
417. C2×C4C2×#10621873semidirect
453. C2#19133537direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835302
C2×#145830522
C2×#145828162
#191335372
C2×#145826372
C2×C43×#3242
C2×#159943