Finite Group Databasebeta

← #24995555

Subgroups — #24995555

Order 11008.

600 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063314C211yesmaximal, characteristic
2C4⋊C8×Dic43C211yesmaximal, characteristic, complemented
3C4×Dic43⋊C8C211yesmaximal, characteristic, complemented
4C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
5C2×#14582628C211yesmaximal, characteristic
6C2×#14582626C211yesmaximal, characteristic
7C2×C43×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#13063314C411yescharacteristic
9C2×C4×D172C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×Dic43⋊C8—21no—
12C2×C4×C43⋊C8C2211yescharacteristic
13C2×C8×Dic43—21no—
14#14582806C411yescharacteristic
15#14582800C411yescharacteristic
16#14582789—21no—
17#14582789—21no—
18#14582764C411yescharacteristic
19C4×(C2×D43)⋊C4—21no—
20C4×(C2×D43)⋊C4—21no—
21C42×Dic43C2211yescharacteristic
22#14582653—21no—
23#14582653—21no—
24Q8⋊(C43⋊C8)—22no—
25#14582628—22no—
26#14582626—22no—
27C2×C4×Q8×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4×C8×C43C2211yescharacteristic
30C43×Q8⋊C8—22no—
31C22×D172C2×C411yescharacteristic
32C22×C4×D43—21no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35#13063314—22no—
36#13063314C814yescomplemented
37C4×D172—21no—
38C4×D172—21no—
39C4×D172—21no—
40C4×D172—21no—
41C2×C4⋊Dic43C2×C411yescharacteristic
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×C4×Dic43C2×C411yescharacteristic
48C2×C4×Dic43C2×C411yescharacteristic
49C2×C4×Dic43D411yescharacteristic
50C2×C4×Dic43D411yescharacteristic
51C2×C4×Dic43D411yescharacteristic
52C2×C4×Dic43D411yescharacteristic
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)D412yes—
55Dic43⋊C8—24no—
56C4×C43⋊C8—21no—
57C4×C43⋊C8—21no—
58C8×Dic43—42no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C22×Q8×C43C2×C411yescharacteristic
64C22×C8×C43—21no—
65C22×C8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43C2×C411yescharacteristic
72C2×C42×C43—21no—
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43—21no—
75C4⋊C8×C43D412yes—
76C4×C8×C43—21no—
77C4×C8×C43—21no—
78C23×D43—21no—
79C2×Q8×C43—21no—
80C2×Q8×C43—21no—
81C2×Q8×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43C2×C812yes—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43C22×C411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×Dic43—21no—
91C22×Dic43C22⋊C411yescharacteristic
92C22×Dic43C22⋊C411yescharacteristic
93C22×Dic43C22⋊C411yescharacteristic
94C22×Dic43C22⋊C411yescharacteristic
95C2×D172—21no—
96C2×D172—21no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172—21no—
100C2×D172C2×C812yes—
101C2×C4×D43—41no—
102C2×C4×D43—41no—
103C2×C4×D43—41no—
104C2×C4×D43—41no—
105C2×C4×D43—41no—
106C2×C4×D43—41no—
107C2×C8×C43—22no—
108C2×C8×C43—22no—
109C2×C8×C43—41no—
110C2×C8×C43—41no—
111C2×C8×C43—41no—
112C2×C8×C43—41no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—41no—
117C42×C43—41no—
118C42×C43—41no—
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122C42×C43#4111yescharacteristic
123(C2×D43)⋊C4—24no—
124(C2×D43)⋊C4—24no—
125(C2×D43)⋊C4—42no—
126(C2×D43)⋊C4—41no—
127(C2×D43)⋊C4—41no—
128(C2×D43)⋊C4—42no—
129C4⋊Dic43—21no—
130C4⋊Dic43—21no—
131C4×Dic43—21no—
132C4×Dic43—21no—
133C4×Dic43—21no—
134C4×Dic43—21no—
135C4×Dic43—21no—
136C4×Dic43—21no—
137C4×Dic43—22no—
138C4×Dic43—41no—
139C4×Dic43C2×C812yes—
140C4×Dic43M1612yes—
141C2×C43⋊C8—22no—
142C2×C43⋊C8—22no—
143C2×C43⋊C8—41no—
144C2×C43⋊C8—41no—
145C2×C43⋊C8—41no—
146C2×C43⋊C8—41no—
147C23×C43C2×C22⋊C411yescharacteristic
148C22×D43—22no—
149C22×D43—41no—
150C22×D43—41no—
151C22×D43—41no—
152C22×D43—41no—
153C22×D43—41no—
154C22×D43—41no—
155Q8×C43—22no—
156Q8×C43—22no—
157Q8×C43—41no—
158Q8×C43—41no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—22no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43C4×D411yescharacteristic
168C2×C4×C43C4×D411yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43#12411yescharacteristic
172C2×C4×C43#12711yescharacteristic
173C2×C4×C43C22×C811yescharacteristic
174C2×C4×C43C2×M1611yescharacteristic
175C2×C4×C43#13111yescharacteristic
176C2×C4×C43#13111yescharacteristic
177C2×C4×C43#13511yescharacteristic
178C2×C4×C43#13511yescharacteristic
179C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C43#13711yescharacteristic
181C2×Dic43—21no—
182C2×Dic43—21no—
183C2×Dic43—21no—
184C2×Dic43—21no—
185C2×Dic43—21no—
186C2×Dic43—21no—
187C2×Dic43—21no—
188C2×Dic43—21no—
189C2×Dic43—21no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—41no—
193C2×Dic43C22⋊C812yes—
194C2×Dic43C22⋊C812yes—
195C2×Dic43#10412yes—
196D172—22no—
197D172—22no—
198D172—41no—
199D172—41no—
200C4×D43—81no—
201C4×D43—81no—
202C4×D43—81no—
203C4×D43—81no—
204C8×C43—42no—
205C8×C43—42no—
206C43⋊C8—42no—
207C43⋊C8—42no—
208#9675—431nomaximal, Sylow
209C22×C43#39011yescharacteristic
210C22×C43C2×C22⋊C811yescharacteristic
211C22×C43#40811yescharacteristic
212C22×C43#41611yescharacteristic
213C22×C43#41711yescharacteristic
214C22×C43C2×#10411yescharacteristic
215C22×C43#42111yescharacteristic
216C2×D43—42no—
217C2×D43—42no—
218C2×D43—42no—
219C2×D43—81no—
220C2×D43—81no—
221C2×D43—81no—
222C2×D43—81no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—42no—
226C4×C43—81no—
227C4×C43C8×D411yescharacteristic
228C4×C43C8×D411yescharacteristic
229C4×C43#43611yescharacteristic
230C4×C43#43611yescharacteristic
231C4×C43#46311yescharacteristic
232C4×C43#46311yescharacteristic
233C4×C43#46411yescharacteristic
234C4×C43#46411yescharacteristic
235Dic43—22no—
236Dic43—22no—
237Dic43—22no—
238Dic43—41no—
239Dic43—81no—
240C4×#124—431no—
241C4×C4⋊C8—431no—
242C4×C4⋊C8—431no—
243C2×Q8⋊C8—431no—
244C2×Q8⋊C8D4311yescharacteristic, complemented
245C2×D4⋊C8—431no—
246C2×D4⋊C8—431no—
247C2×C43#147611yescharacteristic
248C2×C43#147711yescharacteristic
249C2×C43#148211yescharacteristic
250C2×C43#148311yescharacteristic
251C2×C43#195411yescharacteristic
252C2×C43#198011yescharacteristic
253C2×C43#198311yescharacteristic
254D43—82no—
255C2×#124—431no—
256C2×C4×Q8C2×D4311yescharacteristic
257C2×C4×D4—431no—
258C2×C4⋊C8—431no—
259C2×C4⋊C8—861no—
260C2×C4⋊C8C2×D4311yescharacteristic
261C2×C4×C8—431no—
262C2×C4×C8—861no—
263C2×C4×C8C2×D4311yescharacteristic
264#391—431no—
265#390—431no—
266#388—861no—
267#388—861no—
268#382—431no—
269C4×C22⋊C4—861no—
270C4×C22⋊C4—861no—
271C43—431no—
272#336—861no—
273#336—861no—
274Q8⋊C8—22no—
275Q8⋊C8—862no—
276D4⋊C8—862no—
277D4⋊C8—862no—
278C43#967511yescharacteristic, complemented, Sylow
279C22×Q8C4×D4311yescharacteristic
280C22×D4—431no—
281C23×C4—861no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—861no—
285C22×C8—861no—
286#124—434no—
287#124—862no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×D4—861no—
293C4×D4—861no—
294C4×D4—861no—
295C4×D4—861no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—431no—
298C2×C4⋊C4C4×D4311yescharacteristic
299C2×C22⋊C4—861no—
300C2×C22⋊C4—861no—
301C2×C22⋊C4—861no—
302C2×C22⋊C4—861no—
303C2×C22⋊C4—861no—
304C2×C42—21no—
305C2×C42—431no—
306C2×C42—431no—
307C2×C42—431no—
308C2×C42—431no—
309C2×C42—431no—
310C2×C42—431no—
311C2×C42C22×D4311yescharacteristic
312C4⋊C8—21no—
313C4⋊C8—432no—
314C4⋊C8—864no—
315C4⋊C8—861no—
316C4⋊C8C22⋊D4312yes—
317C4×C8—21no—
318C4×C8—21no—
319C4×C8—861no—
320C4×C8—861no—
321C4×C8—1722no—
322#95—861no—
323#95—861no—
324#95—861no—
325#95—861no—
326C24—861no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8C8×D4312yes—
333C2×D4—432no—
334C2×D4—861no—
335C2×D4—861no—
336C2×D4—861no—
337C2×D4—861no—
338C2×D4—861no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—431no—
342C22×C4—431no—
343C22×C4—431no—
344C22×C4—431no—
345C22×C4—861no—
346C22×C4—1721no—
347C22×C4—1721no—
348C22×C4—1721no—
349C22×C4—1721no—
350C22×C4—1721no—
351C22×C4—1721no—
352C22×C4C2×C4×D4311yescharacteristic
353C22×C4D4×D4311yescharacteristic
354C22×C4D4×D4311yescharacteristic
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—862no—
362C2×C8—862no—
363C2×C8—1721no—
364C2×C8—1721no—
365C2×C8—1721no—
366C2×C8—1721no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—861no—
372C4⋊C4—861no—
373C22⋊C4—864no—
374C22⋊C4—864no—
375C22⋊C4—1722no—
376C22⋊C4—1722no—
377C22⋊C4—1721no—
378C22⋊C4—1721no—
379C42—41no—
380C42—41no—
381C42—432no—
382C42—432no—
383C42—862no—
384C42—861no—
385C42—861no—
386C42—861no—
387C42—861no—
388C42—861no—
389C42—861no—
390C42—1721no—
391C42#1062189811yescharacteristic
392C42D4×D4311yescharacteristic
393C42#1062190011yescharacteristic
394C42C2×C22⋊D4311yescharacteristic
395C23—862no—
396C23—1721no—
397C23—1721no—
398C23—1721no—
399C23—1721no—
400C23—1721no—
401C23—1721no—
402C23C22⋊C4×D4311yescharacteristic
403Q8—22no—
404Q8—22no—
405Q8—41no—
406Q8—41no—
407D4—862no—
408D4—862no—
409D4—1721no—
410D4—1721no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—432no—
420C2×C4—432no—
421C2×C4—432no—
422C2×C4—861no—
423C2×C4—861no—
424C2×C4—861no—
425C2×C4—861no—
426C2×C4—861no—
427C2×C4—861no—
428C2×C4—861no—
429C2×C4—861no—
430C2×C4—861no—
431C2×C4—3441no—
432C2×C4—3441no—
433C2×C4—3441no—
434C2×C4—3441no—
435C2×C4—1721no—
436C2×C4—1721no—
437C2×C4—1721no—
438C2×C4(C22⋊D43)⋊C411yescharacteristic
439C2×C4C4×C22⋊D4311yescharacteristic
440C2×C4#1306329711yescharacteristic
441C2×C4#1306329811yescharacteristic
442C2×C4#1306331111yescharacteristic
443C2×C4#1306332111yescharacteristic
444C2×C4C2×C8×D4311yescharacteristic
445C2×C4M16×D4311yescharacteristic
446C2×C4#1306333111yescharacteristic
447C2×C4#1306333311yescharacteristic
448C2×C4#1306334611yescharacteristic
449C2×C4#1306334811yescharacteristic
450C2×C4#1306335211yescharacteristic
451C2×C4#1306335711yescharacteristic
452C8—42no—
453C8—42no—
454C8—1722no—
455C8—1722no—
456C22—3441no—
457C22—3441no—
458C22—3441no—
459C22—3441no—
460C22—1722no—
461C22—1722no—
462C22—1722no—
463C22#1458279911yescharacteristic
464C22C22⋊C8×D4311yescharacteristic
465C22#1458286411yescharacteristic
466C22#1458289411yescharacteristic
467C22#1458289911yescharacteristic
468C22#104×D4311yescharacteristic
469C22#1458291411yescharacteristic
470C4—21no—
471C4—21no—
472C4—42no—
473C4—81no—
474C4—862no—
475C4—862no—
476C4—862no—
477C4—3441no—
478C4—1721no—
479C4(C22⋊D43)⋊C811yescharacteristic
480C4C8×C22⋊D4311yescharacteristic
481C4#1458297411yescharacteristic
482C4#1458297511yescharacteristic
483C4#1458311611yescharacteristic
484C4#1458311711yescharacteristic
485C4#1458312311yescharacteristic
486C4#1458312411yescharacteristic
487C2—3442no—
488C2#1913297611yescharacteristic
489C2#1913298111yescharacteristic
490C2#1913300211yescharacteristic
491C2#1913300711yescharacteristic
492C2#1913538711yescharacteristic
493C2#1913551211yescharacteristic
494C2#1913552411yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC2×C43×Q8⋊C8C2
socleC23×C43C2×C22⋊C4
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenterC2×Q8⋊C8D43
hypocenterC43#9675
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×Dic43C2semidirect
3. C4×Dic43⋊C8C2semidirect
4. C2×Q8⋊(C43⋊C8)C2semidirect
7. C2×C43×Q8⋊C8C2semidirect
36. #13063314C8semidirect
244. C2×Q8⋊C8D43semidirect
278. C43#9675semidirect

Maximal subgroups

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

subgroupindex
C4×#130633142
C4⋊C8×Dic432
C4×Dic43⋊C82
C2×Q8⋊(C43⋊C8)2
C2×#145826282
C2×#145826262
C2×C43×Q8⋊C82
#967543