Finite Group Databasebeta

← C2×#19133600 #25068816

Subgroups — C2×#19133600 #25068816

Order 11008.

1308 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1308 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×#14583480C211yesmaximal, characteristic
2C2×#14583213C212yesmaximal, complemented
3C2×#14582829C211yesmaximal, characteristic, complemented
4#19133600C218yesmaximal, direct product factor
5C2×#14582634C212yesmaximal, complemented
6C2×C43×#324C211yesmaximal, characteristic, complemented
7C22×#10621898—21no—
8#14583480—24no—
9#14583480—22no—
10#14583480C2214yes—
11C2×#13063305—22no—
12C2×#13063300—22no—
13C2×#13063299—21no—
14C2×#13063299C2212yes—
15C22×C4⋊Dic43C2211yescharacteristic
16C22×Dic43⋊C4—21no—
17#14583213—24no—
18#14583213C2218yescomplemented
19C2×#13063259—22no—
20C2×#13063247—22no—
21#14582829—22no—
22#14582829C2214yescomplemented
23C2×C43⋊#95—21no—
24C2×C43⋊#95C2211yescharacteristic
25#14582634C2218yescomplemented
26C22×C4⋊C4×C43C2211yescharacteristic
27C2×C22⋊C8×C43C2212yes—
28C43×#324C2214yescomplemented
29C2×#10621898—24no—
30C2×#10621898—24no—
31C2×#10621898—44no—
32C2×#10621898—44no—
33C22×Dic86—21no—
34C22×D172—21no—
35C22×D172—21no—
36C22×D172D412yes—
37C22×C22⋊D43—22no—
38C23×Dic43—21no—
39C23×Dic43—21no—
40C22×C4×D43—22no—
41#13063305—28no—
42#13063305—28no—
43#13063300—28no—
44#13063300—28no—
45#13063299—24no—
46#13063299—24no—
47#13063299—22no—
48#13063299—22no—
49#13063299D414yes—
50#13063299C2314yes—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43D412yes—
56C2×C4⋊Dic43C2312yes—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—44no—
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—22no—
61#13063259—28no—
62#13063247—28no—
63C43⋊#95—21no—
64C43⋊#95—24no—
65C43⋊#95C2312yes—
66C23×C4×C43D411yescharacteristic
67C23×C4×C43D411yescharacteristic
68C23×C4×C43C2311yescharacteristic
69C22×C8×C43—22no—
70C2×C4⋊C4×C43—22no—
71C2×C4⋊C4×C43—22no—
72C2×C4⋊C4×C43D412yes—
73C2×C4⋊C4×C43C2312yes—
74C22⋊C8×C43—22no—
75C22⋊C8×C43C2314yes—
76C24×C43C2×D411yescharacteristic
77C23×D43—22no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—22no—
83C22×C4×C43—42no—
84C22×C4×C43—42no—
85C22×C4×C43D814yes—
86C22×C4×C43C2×D412yes—
87C22×C4×C43C2×D412yes—
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2×D412yes—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2411yescharacteristic
92C2×C22⋊D43—24no—
93C2×C22⋊D43—24no—
94C2×C22⋊D43—44no—
95C2×C22⋊D43—44no—
96C22×Dic43—24no—
97C22×Dic43—22no—
98C22×Dic43—22no—
99C22×Dic43—22no—
100C22×Dic43—42no—
101C22×Dic43—41no—
102C22×Dic43—41no—
103C22×Dic43—42no—
104C22×Dic43—42no—
105C22×Dic43—42no—
106#10621898—48no—
107#10621898—416no—
108#10621898—48no—
109C2×D172—24no—
110C2×D172—24no—
111C2×D172—22no—
112C2×D172—44no—
113C2×D172—44no—
114C2×D172—82no—
115C2×D172C2×D414yes—
116C2×C4×D43—28no—
117C2×C4×D43—48no—
118C2×Dic86—24no—
119C2×Dic86—44no—
120C2×C8×C43—24no—
121C2×C8×C43—44no—
122C4⋊C4×C43—24no—
123C4⋊C4×C43—24no—
124(C2×D43)⋊C4—28no—
125(C2×D43)⋊C4—24no—
126(C2×D43)⋊C4—24no—
127C4⋊Dic43—24no—
128C4⋊Dic43—22no—
129C4⋊Dic43—24no—
130C4⋊Dic43—42no—
131C4⋊Dic43C2×D414yes—
132Dic43⋊C4—48no—
133C23×C43—22no—
134C23×C43—22no—
135C23×C43#12011yescharacteristic
136C23×C43#12011yescharacteristic
137C23×C43C2×D812yes—
138C23×C43AGL(1,ℤ/8)12yes—
139C23×C43C22×D411yescharacteristic
140C22×D43—24no—
141C22×D43—44no—
142C22×D43—44no—
143C22×D43—44no—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—24no—
147C2×C4×C43—24no—
148C2×C4×C43—24no—
149C2×C4×C43—22no—
150C2×C4×C43—41no—
151C2×C4×C43—42no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—81no—
156C2×C4×C43#12012yes—
157C2×C4×C43C2×D814yes—
158C2×C4×C43C22×D412yes—
159C22⋊D43—44no—
160C22⋊D43—44no—
161C22⋊D43—48no—
162C2×Dic43—24no—
163C2×Dic43—24no—
164C2×Dic43—48no—
165C2×Dic43—42no—
166C2×Dic43—42no—
167C2×Dic43—44no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—42no—
171C2×Dic43—82no—
172C2×Dic43—82no—
173D172—44no—
174D172—48no—
175D172—82no—
176D172—84no—
177C4×D43—416no—
178Dic86—48no—
179C8×C43—44no—
180C2×#1610—431nomaximal, Sylow
181C22×C43—24no—
182C22×C43—24no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43#44712yes—
188C22×C43#44712yes—
189C22×C43#45612yes—
190C22×C43#45812yes—
191C22×C43C2×#12011yescharacteristic
192C22×C43C22×D811yescharacteristic
193C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
194C2×D43—44no—
195C2×D43—44no—
196C2×D43—44no—
197C2×D43—88no—
198C4×C43—24no—
199C4×C43—22no—
200C4×C43—22no—
201C4×C43—42no—
202Dic43—44no—
203Dic43—44no—
204Dic43—82no—
205C2×#537—431no—
206C2×#480—432no—
207C2×#398—431no—
208#1610—438no—
209C2×#327—432no—
210C2×#324D4311yescharacteristic, complemented
211C2×C43—21no—
212C2×C43—21no—
213C2×C43—22no—
214C2×C43#161014yescomplemented
215C2×C43C2×#44711yescharacteristic
216C2×C43C2×#45611yescharacteristic
217C2×C43C2×#45811yescharacteristic
218D43—84no—
219C22×#41—861no—
220#537—434no—
221#537—864no—
222#537—862no—
223C2×C22⋊Q8—862no—
224C2×#121—432no—
225C2×#121—862no—
226C2×#121—861no—
227C22×C4⋊C4—431no—
228C22×C4⋊C4—861no—
229C22×C4⋊C4C2×D4311yescharacteristic
230#480—438no—
231#480—864no—
232C2×#107—862no—
233C2×#102—862no—
234C2×C22⋊C8C2×D4312yes—
235#398—434no—
236#398—862no—
237C2×#95—431no—
238C2×#95—861no—
239#327—438no—
240#324C2×D4314yescomplemented
241C43C2×#161011yescharacteristic, complemented, Sylow
242C2×#41—864no—
243C2×#41—864no—
244C2×#41—1724no—
245C2×#41—1724no—
246C22×Q8—861no—
247C22×D4—432no—
248C22×D4—861no—
249C22×D4—861no—
250C22×D4—862no—
251C23×C4—862no—
252C23×C4—861no—
253C23×C4—861no—
254C23×C4D17211yescharacteristic
255C23×C4D17211yescharacteristic
256C23×C4C22×D4311yescharacteristic
257C22×C8—22no—
258C22⋊Q8—868no—
259C22⋊Q8—868no—
260#121—434no—
261#121—434no—
262#121—868no—
263#121—868no—
264#121—864no—
265#121—862no—
266#121—864no—
267#121—862no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—432no—
271C2×C4⋊C4—432no—
272C2×C4⋊C4—861no—
273C2×C4⋊C4—862no—
274C2×C4⋊C4—862no—
275C2×C4⋊C4—861no—
276C2×C4⋊C4—864no—
277C2×C4⋊C4—1724no—
278C2×C4⋊C4D17212yes—
279C2×C4⋊C4C22×D4312yes—
280C2×C22⋊C4—862no—
281C2×C22⋊C4—862no—
282#107—868no—
283#102—868no—
284C22⋊C8—22no—
285C22⋊C8C22×D4314yes—
286#95—432no—
287#95—861no—
288#95—864no—
289C24—862no—
290C24C2×D17211yescharacteristic
291#41—1728no—
292#41—17216no—
293#41—1728no—
294C2×Q8—864no—
295C2×Q8—1724no—
296C2×D4—434no—
297C2×D4—864no—
298C2×D4—864no—
299C2×D4—864no—
300C2×D4—864no—
301C2×D4—862no—
302C2×D4—3442no—
303C2×D4—1724no—
304C2×D4—1724no—
305C2×D4—1724no—
306C2×D4—1724no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—868no—
315C22×C4—864no—
316C22×C4—862no—
317C22×C4—862no—
318C22×C4—862no—
319C22×C4—1728no—
320C22×C4—1721no—
321C22×C4—1721no—
322C22×C4—1722no—
323C22×C4—1722no—
324C22×C4—1722no—
325C22×C4—1722no—
326C22×C4D34414yes—
327C22×C4C2×D17212yes—
328C22×C4C2×D17212yes—
329C22×C4C2×D17211yescharacteristic
330C22×C4D4×D4312yes—
331C22×C4D4×D4312yes—
332C22×C4C23×D4311yescharacteristic
333C2×C8—24no—
334C2×C8—44no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—434no—
338C4⋊C4—864no—
339C4⋊C4—862no—
340C4⋊C4—864no—
341C4⋊C4—1722no—
342C4⋊C4—1728no—
343C22⋊C4—868no—
344C22⋊C4—864no—
345C22⋊C4—864no—
346C23—22no—
347C23—22no—
348C23—864no—
349C23—1724no—
350C23—1724no—
351C23—1724no—
352C23#1306329511yescharacteristic
353C23#1306329511yescharacteristic
354C23C2×D34412yes—
355C23#1306335312yes—
356C23C22×D17211yescharacteristic
357Q8—1728no—
358D4—3442no—
359D4—3444no—
360D4—1724no—
361D4—1728no—
362D4—1724no—
363D4—1724no—
364D4—1728no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—864no—
378C2×C4—864no—
379C2×C4—3442no—
380C2×C4—3442no—
381C2×C4—17216no—
382C2×C4—1722no—
383C2×C4—1722no—
384C2×C4—1722no—
385C2×C4—1722no—
386C2×C4—1728no—
387C2×C4—1722no—
388C2×C4—1724no—
389C2×C4#1306329512yes—
390C2×C4C2×D34414yes—
391C2×C4C2×D4×D4312yes—
392C8—44no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—24no—
398C22—24no—
399C22—3448no—
400C22—1724no—
401C22—1724no—
402C22—1724no—
403C22#1458303512yes—
404C22#1458303512yes—
405C22#1458308412yes—
406C22#1458309012yes—
407C22C2×#1306329511yescharacteristic
408C22C22×D34411yescharacteristic
409C22C2×#1306335311yescharacteristic
410C4—22no—
411C4—22no—
412C4—24no—
413C4—42no—
414C4—3442no—
415C4—1724no—
416C4—1724no—
417C2—21no—
418C2—21no—
419C2—22no—
420C2—3444no—
421C2#1913360014yesdirect product factor
422C2C2×#1458303511yescharacteristic
423C2C2×#1458308411yescharacteristic
424C2C2×#1458309011yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#324C2
socleC23×C43#120
prime radicalC2×#14583480C2
hypercenterC2×#324D43
hypocenterC43C2×#1610
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
2. C2×#14583213C2semidirect
3. C2×#14582829C2semidirect
4. #19133600C2direct (N × H)
5. C2×#14582634C2semidirect
6. C2×C43×#324C2semidirect
18. #14583213C22semidirect
22. #14582829C22semidirect
25. #14582634C22semidirect
28. C43×#324C22semidirect
210. C2×#324D43semidirect
214. C2×C43#1610semidirect
240. #324C2×D43semidirect
241. C43C2×#1610semidirect
421. C2#19133600direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834802
C2×#145832132
C2×#145828292
#191336002
C2×#145826342
C2×C43×#3242
C2×#161043