Finite Group Databasebeta

← #24992144

Subgroups — #24992144

Order 11008.

560 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143621C211yesmaximal, characteristic
2#19137264C211yesmaximal, characteristic
3#19132911C211yesmaximal, characteristic
4C2×#14582625C211yesmaximal, characteristic, complemented
5#19132442C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C2×C43×#324C211yesmaximal, characteristic, complemented
8C2×#13063308C411yescharacteristic
9C2×C4×C22⋊D43C2211yescharacteristic
10#14582970—22no—
11#14582967—22no—
12#14582953—21no—
13#14582861—21no—
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16#14582794—21no—
17#14582789—21no—
18#14582780—21no—
19#14582778C411yescharacteristic
20#14582772C411yescharacteristic
21#14582770—21no—
22#14582762C411yescharacteristic
23C4×C22⋊Dic43C2211yescharacteristic
24#14582625—22no—
25#14582624—21no—
26#14582622—21no—
27C22×C4⋊C4×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C43×#324—22no—
31C22×C22⋊D43C2×C411yescharacteristic
32C22×C4×D43D411yescharacteristic
33C2×#10621872—22no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36#13063308—22no—
37#13063308—22no—
38C4×C22⋊D43—21no—
39C4×C22⋊D43—21no—
40C4×C22⋊D43—21no—
41C4×C22⋊D43—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4D411yescharacteristic
45C2×C22⋊Dic43C2×C411yescharacteristic
46C2×C22⋊Dic43C2×C411yescharacteristic
47C2×C22⋊Dic43C2×C411yescharacteristic
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4D411yescharacteristic
51C2×C4×Dic43—21no—
52C2×C4×Dic43D411yescharacteristic
53Dic43⋊C8—22no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)D412yes—
58(C2×D43)⋊C8—22no—
59#13063235—22no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C23×C4×C43C2×C411yescharacteristic
66C23×C4×C43C2×C411yescharacteristic
67C23×C4×C43C2311yescharacteristic
68C22×C8×C43—21no—
69C22×C8×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43D412yes—
80C24×C43C22×C411yescharacteristic
81C23×D43C22⋊C411yescharacteristic
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—81no—
92C22×C4×C43—81no—
93C22×C4×C43M1612yescomplemented
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43#4111yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C2×C22⋊D43—21no—
101C2×C22⋊D43—21no—
102C2×C22⋊D43—21no—
103C2×C22⋊D43—21no—
104C2×C22⋊D43—21no—
105C2×C22⋊D43—21no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43C22⋊C411yescharacteristic
109C22×Dic43C22⋊C411yescharacteristic
110C22×Dic43C22⋊C411yescharacteristic
111C2×C4×D43—21no—
112C2×C4×D43—21no—
113C2×C4×D43—81no—
114C2×C8×C43—22no—
115C2×C8×C43—41no—
116C2×C8×C43—81no—
117C2×C8×C43—81no—
118C4⋊C4×C43—41no—
119C4⋊C4×C43—41no—
120C4⋊C4×C43—41no—
121C4⋊C4×C43—41no—
122C22⋊Dic43—21no—
123C22⋊Dic43—21no—
124C22⋊Dic43—21no—
125C22⋊Dic43—21no—
126C22⋊Dic43—21no—
127C22⋊Dic43M1612yescomplemented
128(C2×D43)⋊C4—24no—
129(C2×D43)⋊C4—21no—
130(C2×D43)⋊C4—21no—
131(C2×D43)⋊C4—81no—
132Dic43⋊C4—24no—
133Dic43⋊C4—21no—
134Dic43⋊C4—21no—
135Dic43⋊C4—81no—
136C4×Dic43—21no—
137C4×Dic43—21no—
138C4×Dic43—81no—
139C2×C43⋊C8—22no—
140C2×C43⋊C8—41no—
141C2×C43⋊C8—81no—
142C2×C43⋊C8—81no—
143#10621872—82no—
144C23×C43—41no—
145C23×C43—41no—
146C23×C43C2×C22⋊C411yescharacteristic
147C23×C43C4×D411yescharacteristic
148C23×C43C4×D411yescharacteristic
149C23×C43C2×M1611yescharacteristic
150C23×C43C2×M1611yescharacteristic
151C23×C43#13111yescharacteristic
152C23×C43#13111yescharacteristic
153C22×D43—21no—
154C22×D43—21no—
155C22×D43—21no—
156C22×D43—41no—
157C22×D43—41no—
158C2×C4×C43—22no—
159C2×C4×C43—22no—
160C2×C4×C43—22no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—81no—
175C2×C4×C43—81no—
176C2×C4×C43#12011yescharacteristic
177C2×C4×C43#12111yescharacteristic
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43#12311yescharacteristic
180C22⋊D43—41no—
181C22⋊D43—41no—
182C22⋊D43—41no—
183C22⋊D43—41no—
184C2×Dic43—21no—
185C2×Dic43—21no—
186C2×Dic43—21no—
187C2×Dic43—21no—
188C2×Dic43—22no—
189C2×Dic43—21no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—41no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C4×D43—42no—
198C4×D43—81no—
199C8×C43—42no—
200C8×C43—81no—
201C43⋊C8—42no—
202C43⋊C8—81no—
203#9110—431nomaximal, Sylow
204C22×C43—21no—
205C22×C43—21no—
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—41no—
211C22×C43—41no—
212C22×C43—41no—
213C22×C43—41no—
214C22×C43#38611yescharacteristic
215C22×C43#40711yescharacteristic
216C22×C43#40811yescharacteristic
217C22×C43#43511yescharacteristic
218C22×C43#43511yescharacteristic
219C22×C43#43611yescharacteristic
220C22×C43#43611yescharacteristic
221C2×D43—42no—
222C2×D43—41no—
223C2×D43—41no—
224C2×D43—41no—
225C2×D43—81no—
226C4×C43—21no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—42no—
231C4×C43—81no—
232Dic43—42no—
233Dic43—41no—
234Dic43—41no—
235Dic43—41no—
236Dic43—81no—
237#2973—431no—
238#2322—431no—
239#1459—431no—
240C2×#324—431no—
241C2×#324D4311yescharacteristic, complemented
242#1282—431no—
243#1282—431no—
244C2×C43—21no—
245C2×C43—21no—
246C2×C43—21no—
247C2×C43—21no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43#187011yescharacteristic
251C2×C43#191311yescharacteristic
252C2×C43#191511yescharacteristic
253D43—81no—
254C2×#123—431no—
255C2×C4×D4—431no—
256C22×C4⋊C4C2×D4311yescharacteristic
257#435—862no—
258#435—862no—
259#432—861no—
260#407—861no—
261C2×C22⋊C8—431no—
262C2×C22⋊C8—431no—
263C2×C22⋊C8C2×D4311yescharacteristic
264C2×C22⋊C8C2×D4311yescharacteristic
265#389—861no—
266#388—861no—
267#387—861no—
268#386—431no—
269#385—431no—
270#385—861no—
271#381—431no—
272C4×C22⋊C4—431no—
273#324—22no—
274#324—861no—
275#324—862no—
276#323—861no—
277C43#911011yescharacteristic, complemented, Sylow
278C22×D4—431no—
279C23×C4—431no—
280C23×C4C4×D4311yescharacteristic
281C23×C4C4×D4311yescharacteristic
282C23×C4C22×D4311yescharacteristic
283C2×M16—862no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—861no—
287C22×C8—861no—
288#123—862no—
289#123—862no—
290C4×D4—861no—
291C4×D4—861no—
292C4×D4—861no—
293C4×D4—861no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—431no—
301C2×C4⋊C4—861no—
302C2×C4⋊C4—861no—
303C2×C22⋊C4—431no—
304C2×C22⋊C4—431no—
305C2×C22⋊C4—431no—
306C2×C22⋊C4—431no—
307C2×C22⋊C4—861no—
308C2×C22⋊C4—861no—
309C2×C42—431no—
310C2×C42—861no—
311C4⋊C8—862no—
312C22⋊C8—21no—
313C22⋊C8—21no—
314C22⋊C8—21no—
315C22⋊C8—432no—
316C22⋊C8—862no—
317C22⋊C8—861no—
318C22⋊C8—861no—
319C22⋊C8—861no—
320C22⋊C8C22⋊D4312yes—
321#97—862no—
322#95—861no—
323#95—861no—
324#95—861no—
325#95—861no—
326#95—861no—
327C24—431no—
328C24C2×C4×D4311yescharacteristic
329C2×D4—861no—
330C2×D4—861no—
331C2×D4—861no—
332C2×D4—861no—
333C2×D4—861no—
334C2×D4—861no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—81no—
345C22×C4—81no—
346C22×C4—431no—
347C22×C4—431no—
348C22×C4—431no—
349C22×C4—861no—
350C22×C4—861no—
351C22×C4—861no—
352C22×C4—861no—
353C22×C4—3441no—
354C22×C4#1062187212yescomplemented
355C22×C4#1062189811yescharacteristic
356C22×C4D4×D4311yescharacteristic
357C22×C4D4×D4311yescharacteristic
358C22×C4D4×D4311yescharacteristic
359C22×C4#1062190011yescharacteristic
360C22×C4C2×C22⋊D4311yescharacteristic
361M16—3442no—
362C2×C8—22no—
363C2×C8—41no—
364C2×C8—81no—
365C2×C8—81no—
366C2×C8—862no—
367C2×C8—3441no—
368C2×C8—3441no—
369C2×C8—1721no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—864no—
375C4⋊C4—861no—
376C4⋊C4—861no—
377C4⋊C4—3441no—
378C22⋊C4—432no—
379C22⋊C4—864no—
380C22⋊C4—861no—
381C22⋊C4—861no—
382C22⋊C4—861no—
383C22⋊C4—861no—
384C22⋊C4—861no—
385C22⋊C4—861no—
386C22⋊C4—861no—
387C22⋊C4—3441no—
388C42—861no—
389C42—861no—
390C42—3441no—
391C23—41no—
392C23—41no—
393C23—861no—
394C23—861no—
395C23—861no—
396C23—1721no—
397C23—1721no—
398C23C22⋊C4×D4311yescharacteristic
399C23(C22⋊D43)⋊C411yescharacteristic
400C23C4×C22⋊D4311yescharacteristic
401C23M16×D4311yescharacteristic
402C23C2×#1062187211yescharacteristic
403C23#1306333111yescharacteristic
404C23#1306333311yescharacteristic
405D4—1721no—
406D4—1721no—
407D4—1721no—
408D4—1721no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—862no—
428C2×C4—861no—
429C2×C4—861no—
430C2×C4—861no—
431C2×C4—861no—
432C2×C4—861no—
433C2×C4—3441no—
434C2×C4—1722no—
435C2×C4—1721no—
436C2×C4—1721no—
437C2×C4—1721no—
438C2×C4—1721no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4#1306329311yescharacteristic
443C2×C4#1306329611yescharacteristic
444C2×C4#1306329811yescharacteristic
445C2×C4#1306330711yescharacteristic
446C8—42no—
447C8—81no—
448C8—3441no—
449C8—1722no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—3441no—
461C22—1722no—
462C22—1721no—
463C22—1721no—
464C22—1721no—
465C22#1458277511yescharacteristic
466C22#1458286111yescharacteristic
467C22#1458286411yescharacteristic
468C22#1458296711yescharacteristic
469C22#1458297011yescharacteristic
470C22#1458297411yescharacteristic
471C22#1458297511yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—42no—
477C4—81no—
478C4—3441no—
479C4—1722no—
480C4—1721no—
481C4—1721no—
482C4—1721no—
483C2—21no—
484C2—21no—
485C2—21no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—3441no—
490C2#1913488911yescharacteristic
491C2#1913513411yescharacteristic
492C2#1913514411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#324C2
socleC22×C43#386
prime radicalC22×C22⋊D43C2×C4
cosocleC23×C4×C43C23
hypercenterC2×#324D43
hypocenterC43#9110
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
4. C2×#14582625C2semidirect
5. #19132442C2semidirect
6. #19132441C2semidirect
7. C2×C43×#324C2semidirect
93. C22×C4×C43M16semidirect
127. C22⋊Dic43M16semidirect
241. C2×#324D43semidirect
277. C43#9110semidirect
354. C22×C4#10621872semidirect

Maximal subgroups

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

subgroupindex
#191436212
#191372642
#191329112
C2×#145826252
#191324422
#191324412
C2×C43×#3242
#911043