Finite Group Databasebeta

← C2×#19133638 #25068833

Subgroups — C2×#19133638 #25068833

Order 11008.

984 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583528C211yesmaximal, characteristic
2C2×#14583235C211yesmaximal, characteristic
3C2×#14583232C211yesmaximal, characteristic
4C2×#14582839C211yesmaximal, characteristic
5#19133638C218yesmaximal, direct product factor
6C2×#14582635C211yesmaximal, characteristic
7C2×#14582624C211yesmaximal, characteristic
8C2×C43×#328C211yesmaximal, characteristic
9#14583528—22no—
10#14583528—22no—
11#14583528—22no—
12#14583528C2214yes—
13C2×#13063324—21no—
14C2×#13063323—21no—
15C2×#13063315—21no—
16C2×#13063315—21no—
17C2×#13063304C2211yescharacteristic
18C2×#13063302—21no—
19C2×#13063281—21no—
20C22×C4⋊Dic43C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22#14583235—22no—
23#14583235C2214yes—
24#14583232—22no—
25#14583232C2214yes—
26C2×#13063259—21no—
27C2×#13063258—21no—
28C2×#13063250—21no—
29C2×#13063249—21no—
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31#14582839—22no—
32#14582839C2214yes—
33C2×C43⋊#95—21no—
34C2×C43⋊#95—21no—
35#14582635C2214yes—
36#14582624C2214yes—
37C2×C22⋊Q8×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C43×#328C2214yes—
41C22×Dic86—21no—
42C22×Dic86D411yescharacteristic
43C23×Dic43—21no—
44C23×Dic43D411yescharacteristic
45C23×Dic43D411yescharacteristic
46C22×C43⋊C8—21no—
47#13063324—24no—
48#13063324—24no—
49#13063323—24no—
50#13063323—24no—
51#13063315—24no—
52#13063315—24no—
53#13063315—24no—
54#13063315—24no—
55#13063304—21no—
56#13063304—21no—
57#13063304D412yes—
58#13063304C2312yes—
59#13063302—24no—
60#13063302—24no—
61#13063281—24no—
62#13063281—24no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43C2312yes—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D412yes—
81C2×Dic43⋊C4C2312yes—
82C2×C22⋊Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85#13063259—24no—
86#13063258—24no—
87#13063250—24no—
88#13063249—24no—
89C22⋊(C43⋊C8)—21no—
90C22⋊(C43⋊C8)C2312yes—
91C43⋊#95—24no—
92C43⋊#95—24no—
93C22×Q8×C43D411yescharacteristic
94C23×C4×C43—21no—
95C23×C4×C43C2311yescharacteristic
96C22×C8×C43—21no—
97C22⋊Q8×C43—21no—
98C22⋊Q8×C43—21no—
99C22⋊Q8×C43D412yes—
100C22⋊Q8×C43C2312yes—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C22⋊C4×C43—21no—
104C22⋊C8×C43—21no—
105C22⋊C8×C43C2312yes—
106#95×C43—21no—
107#95×C43C2312yes—
108C24×C43C2×D411yescharacteristic
109C2×Q8×C43—21no—
110C2×Q8×C43—42no—
111C2×Q8×C43C2×D412yes—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43—42no—
116C22×C4×C43—42no—
117C22×C4×C43—42no—
118C22×C4×C43—42no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2411yescharacteristic
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—42no—
134C22×Dic43—44no—
135C22×Dic43—41no—
136C22×Dic43—41no—
137C22×Dic43Q1614yes—
138C22×Dic43C2×D412yes—
139C22×Dic43C2×D412yes—
140C2×Dic86—24no—
141C2×Dic86—21no—
142C2×Dic86—42no—
143C2×Dic86—82no—
144C2×Dic86C2×D412yes—
145C2×C8×C43—22no—
146C2×C8×C43—42no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43C2×D412yes—
151C22⋊C4×C43—22no—
152C22⋊C4×C43—22no—
153C22⋊Dic43—22no—
154C22⋊Dic43—22no—
155C4⋊Dic43—24no—
156C4⋊Dic43—21no—
157C4⋊Dic43—22no—
158C4⋊Dic43—22no—
159C4⋊Dic43—41no—
160C4⋊Dic43—41no—
161C4⋊Dic43C2×D412yes—
162Dic43⋊C4—24no—
163Dic43⋊C4—24no—
164Dic43⋊C4—24no—
165Dic43⋊C4—24no—
166Dic43⋊C4—22no—
167Dic43⋊C4—22no—
168Dic43⋊C4—22no—
169Dic43⋊C4—22no—
170Dic43⋊C4—22no—
171Dic43⋊C4—22no—
172C4×Dic43—24no—
173C4×Dic43—24no—
174C2×C43⋊C8—22no—
175C2×C43⋊C8—42no—
176C23×C43—22no—
177C23×C43—22no—
178C23×C43#12011yescharacteristic
179C23×C43#12011yescharacteristic
180C23×C43C2×Q1612yes—
181C23×C43#13712yes—
182C23×C43C22×D411yescharacteristic
183Q8×C43—42no—
184Q8×C43—81no—
185C2×C4×C43—22no—
186C2×C4×C43—22no—
187C2×C4×C43—22no—
188C2×C4×C43—22no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—84no—
199C2×C4×C43#12011yescharacteristic
200C2×C4×C43#12011yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C2×Dic43—22no—
204C2×Dic43—22no—
205C2×Dic43—24no—
206C2×Dic43—24no—
207C2×Dic43—22no—
208C2×Dic43—22no—
209C2×Dic43—22no—
210C2×Dic43—42no—
211C2×Dic43—42no—
212C2×Dic43—42no—
213C2×Dic43—42no—
214C2×Dic43—44no—
215C2×Dic43—42no—
216C2×Dic43—81no—
217C2×Dic43—82no—
218C2×Dic43—82no—
219C2×Dic43C2×Q1614yes—
220Dic86—42no—
221Dic86—81no—
222Dic86—84no—
223C8×C43—42no—
224C43⋊C8—42no—
225C2×#1617—431nomaximal, Sylow
226C22×C43—24no—
227C22×C43—24no—
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—21no—
232C22×C43#45112yes—
233C22×C43#45112yes—
234C22×C43#45412yes—
235C22×C43#45812yes—
236C22×C43C2×#12011yescharacteristic
237C22×C43C22×Q1611yescharacteristic
238C22×C43C2×#13711yescharacteristic
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—21no—
242C4×C43—21no—
243C4×C43—42no—
244C4×C43—42no—
245C4×C43—82no—
246Dic43—24no—
247Dic43—42no—
248Dic43—42no—
249Dic43—42no—
250Dic43—82no—
251C2×#544—431no—
252C2×#484—431no—
253C2×#484—431no—
254C2×#400—431no—
255#1617—438no—
256C2×#328—431no—
257C2×#328D4311yescharacteristic
258C2×#324—431no—
259C2×C43—21no—
260C2×C43—21no—
261C2×C43—22no—
262C2×C43#161714yescomplemented
263C2×C43C2×#45111yescharacteristic
264C2×C43C2×#45411yescharacteristic
265C2×C43C2×#45811yescharacteristic
266#544—434no—
267#544—862no—
268#544—862no—
269#544—862no—
270C2×C4⋊Q8—861no—
271C2×C4⋊Q8—861no—
272C2×#125—861no—
273C2×#125—861no—
274C2×C22⋊Q8—431no—
275C2×C22⋊Q8—861no—
276C2×C22⋊Q8C2×D4311yescharacteristic
277C2×#117—861no—
278C22×C4⋊C4—431no—
279C22×C4⋊C4—431no—
280#484—434no—
281#484—434no—
282#484—862no—
283#484—862no—
284C2×#107—861no—
285C2×#107—861no—
286C2×#103—861no—
287C2×#103—861no—
288C2×C22⋊C8—431no—
289C2×C22⋊C8C2×D4311yescharacteristic
290#400—434no—
291#400—862no—
292C2×#95—861no—
293C2×#95—861no—
294C2×#95C2×D4311yescharacteristic
295#328—434no—
296#328C2×D4314yes—
297#324—434no—
298C43C2×#161711yescharacteristic, complemented, Sylow
299C22×Q8—431no—
300C22×Q8—861no—
301C22×Q8D17211yescharacteristic
302C23×C4—21no—
303C23×C4—431no—
304C23×C4—431no—
305C23×C4—861no—
306C23×C4C22×D4311yescharacteristic
307C22×C8—21no—
308C22×C8—861no—
309C4⋊Q8—864no—
310C4⋊Q8—864no—
311C4⋊Q8—864no—
312C4⋊Q8—864no—
313#125—864no—
314#125—864no—
315#125—864no—
316#125—864no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—432no—
320C22⋊Q8—432no—
321C22⋊Q8—864no—
322C22⋊Q8—864no—
323C22⋊Q8—861no—
324C22⋊Q8—861no—
325C22⋊Q8D17212yes—
326C22⋊Q8C22×D4312yes—
327#117—864no—
328#117—864no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—431no—
331C2×C4⋊C4—432no—
332C2×C4⋊C4—432no—
333C2×C4⋊C4—432no—
334C2×C4⋊C4—861no—
335C2×C4⋊C4—861no—
336C2×C4⋊C4—861no—
337C2×C4⋊C4—861no—
338C2×C4⋊C4—861no—
339C2×C4⋊C4—861no—
340C2×C4⋊C4—861no—
341C2×C4⋊C4—861no—
342C2×C4⋊C4—861no—
343C2×C4⋊C4—861no—
344C2×C4⋊C4—861no—
345C2×C4⋊C4—861no—
346C2×C4⋊C4—861no—
347C2×C4⋊C4—861no—
348C2×C4⋊C4—861no—
349C2×C4⋊C4D17211yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—861no—
352C2×C42—861no—
353C2×C42—861no—
354#107—864no—
355#107—864no—
356#103—864no—
357#103—864no—
358C22⋊C8—21no—
359C22⋊C8—432no—
360C22⋊C8—861no—
361C22⋊C8C22×D4312yes—
362#95—21no—
363#95—864no—
364#95—864no—
365#95C22×D4312yes—
366C24D4×D4311yescharacteristic
367C2×Q8—21no—
368C2×Q8—42no—
369C2×Q8—432no—
370C2×Q8—864no—
371C2×Q8—861no—
372C2×Q8—3442no—
373C2×Q8—1722no—
374C2×Q8C2×D17212yes—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—434no—
383C22×C4—432no—
384C22×C4—432no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—862no—
388C22×C4—861no—
389C22×C4—861no—
390C22×C4—861no—
391C22×C4—861no—
392C22×C4—862no—
393C22×C4—1724no—
394C22×C4—1721no—
395C22×C4—1721no—
396C22×C4—1722no—
397C22×C4C2×D17211yescharacteristic
398C22×C4C2×D17211yescharacteristic
399C22×C4D4×D4311yescharacteristic
400C22×C4D4×D4311yescharacteristic
401C22×C4D4×D4311yescharacteristic
402C22×C4C23×D4311yescharacteristic
403C2×C8—22no—
404C2×C8—42no—
405C2×C8—862no—
406C2×C8—1722no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—432no—
411C4⋊C4—864no—
412C4⋊C4—864no—
413C4⋊C4—864no—
414C4⋊C4—864no—
415C4⋊C4—864no—
416C4⋊C4—862no—
417C4⋊C4—862no—
418C4⋊C4—861no—
419C4⋊C4—862no—
420C4⋊C4—862no—
421C4⋊C4—862no—
422C4⋊C4—862no—
423C4⋊C4—862no—
424C4⋊C4—862no—
425C4⋊C4—1721no—
426C4⋊C4—1721no—
427C4⋊C4C2×D17212yes—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—862no—
431C22⋊C4—862no—
432C42—864no—
433C42—864no—
434C23—22no—
435C23—22no—
436C23#1306329511yescharacteristic
437C23#1306329511yescharacteristic
438C23Q16×D4312yes—
439C23#1306335412yes—
440C23C2×D4×D4311yescharacteristic
441Q8—42no—
442Q8—81no—
443Q8—3441no—
444Q8—3444no—
445Q8—1722no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—84no—
460C2×C4—434no—
461C2×C4—864no—
462C2×C4—864no—
463C2×C4—862no—
464C2×C4—862no—
465C2×C4—862no—
466C2×C4—862no—
467C2×C4—862no—
468C2×C4—3442no—
469C2×C4—3442no—
470C2×C4—3441no—
471C2×C4—1724no—
472C2×C4—1722no—
473C2×C4—1722no—
474C2×C4—1722no—
475C2×C4—1722no—
476C2×C4—1722no—
477C2×C4#1306329511yescharacteristic
478C2×C4#1306329511yescharacteristic
479C2×C4C2×D4×D4311yescharacteristic
480C2×C4C22×D17211yescharacteristic
481C8—42no—
482C8—1722no—
483C22—21no—
484C22—21no—
485C22—24no—
486C22—24no—
487C22—21no—
488C22—21no—
489C22#1458305612yes—
490C22#1458305612yes—
491C22#1458307312yes—
492C22#1458309012yes—
493C22C2×#1306329511yescharacteristic
494C22C2×Q16×D4311yescharacteristic
495C22C2×#1306335411yescharacteristic
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—42no—
501C4—42no—
502C4—82no—
503C4—864no—
504C4—3442no—
505C4—1722no—
506C4—1722no—
507C4—1722no—
508C2—21no—
509C2—22no—
510C2—21no—
511C2#1913363814yesdirect product factor
512C2C2×#1458305611yescharacteristic
513C2C2×#1458307311yescharacteristic
514C2C2×#1458309011yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#328C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenterC2×#328D43
hypocenterC43C2×#1617
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
5. #19133638C2direct (N × H)
262. C2×C43#1617semidirect
298. C43C2×#1617semidirect
511. C2#19133638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835282
C2×#145832352
C2×#145832322
C2×#145828392
#191336382
C2×#145826352
C2×#145826242
C2×C43×#3282
C2×#161743