Finite Group Databasebeta

← #25016278

Subgroups — #25016278

Order 11008.

484 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 81 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
1#19142538C211yesmaximal, characteristic
2#19134878C211yesmaximal, characteristic
3#19134875C211yesmaximal, characteristic
4#19134807C211yesmaximal, characteristic
5#19132719C211yesmaximal, characteristic
6#19132714C211yesmaximal, characteristic
7C43×#1390C211yesmaximal, characteristic
8#14583374C2211yescharacteristic
9#14582941—21no—
10C2×#13063240C2211yescharacteristic
11#14582841—21no—
12#14582811—21no—
13#14582811—21no—
14#14582803—21no—
15#14582802C2211yescharacteristic
16#14582779C2211yescharacteristic
17#14582774—21no—
18#14582772—21no—
19#14582772—21no—
20#14582771—21no—
21#14582665—21no—
22#14582665—21no—
23#14582660—21no—
24C2×#100×C43C2211yescharacteristic
25C2×#99×C43C2211yescharacteristic
26C43×#386C2211yescharacteristic
27C22×Dic86—21no—
28C23×Dic43D411yescharacteristic
29D4×Dic43—41no—
30D4×Dic43—41no—
31#13063284—21no—
32C2×C4⋊Dic43—41no—
33C2×C4⋊Dic43D411yescharacteristic
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—41no—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43D411yescharacteristic
44C2×C4×Dic43D411yescharacteristic
45#13063259—41no—
46#13063257—41no—
47#13063240—21no—
48#13063240Q812yescomplemented
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—41no—
56C43⋊#95—41no—
57C22×D4×C43C2311yescharacteristic
58C23×C4×C43D411yescharacteristic
59C2×M16×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43D411yescharacteristic
63#100×C43—21no—
64#100×C43Q812yescomplemented
65#99×C43—21no—
66#99×C43Q812yescomplemented
67#95×C43—21no—
68C24×C43C2×D411yescharacteristic
69C24×C43C2×D411yescharacteristic
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43C2×Q811yescharacteristic
73C2×D4×C43C2×Q811yescharacteristic
74C2×D4×C43C2×Q811yescharacteristic
75C2×D4×C43#4111yescharacteristic
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—41no—
79C22×C4×C43—41no—
80C22×C4×C43—81no—
81C22×C4×C43C2×D411yescharacteristic
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—41no—
91C22×Dic43—41no—
92C22×Dic43—81no—
93C2×Dic86—42no—
94C2×Dic86—81no—
95C2×Dic86—81no—
96M16×C43—22no—
97M16×C43—41no—
98C2×C8×C43—41no—
99C22⋊C4×C43—22no—
100C22⋊C4×C43—41no—
101C22⋊C4×C43—41no—
102C22⋊C4×C43—81no—
103C22⋊Dic43—22no—
104C22⋊Dic43—41no—
105C22⋊Dic43—41no—
106C22⋊Dic43—41no—
107C22⋊Dic43—41no—
108C22⋊Dic43—42no—
109C22⋊Dic43—42no—
110C22⋊Dic43—41no—
111C22⋊Dic43—81no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—41no—
115C4⋊Dic43—82no—
116Dic43⋊C4—81no—
117Dic43⋊C4—81no—
118Dic43⋊C4—82no—
119C4×Dic43—41no—
120C4×Dic43—41no—
121C23×C43—21no—
122C23×C43—21no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43#12011yescharacteristic
130C23×C43C22⋊Q811yescharacteristic
131C23×C43C22⋊Q811yescharacteristic
132C23×C43C4⋊Q811yescharacteristic
133C23×C43C4⋊Q811yescharacteristic
134D4×C43—41no—
135D4×C43—41no—
136D4×C43—41no—
137D4×C43—41no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—81no—
149C2×C4×C43—81no—
150C2×C4×C43—81no—
151C2×C4×C43C22⋊Q811yescharacteristic
152C2×C4×C43C4⋊Q811yescharacteristic
153C2×Dic43—22no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—42no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—42no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—81no—
170C2×Dic43—81no—
171C2×Dic43—81no—
172C2×Dic43—81no—
173C2×Dic43—81no—
174C2×Dic43—81no—
175C2×Dic43—81no—
176Dic86—84no—
177C8×C43—42no—
178#13463—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—81no—
194C22×C43—81no—
195C22×C43#39511yescharacteristic
196C22×C43B(4,𝔽2)11yescharacteristic
197C22×C43#45811yescharacteristic
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—81no—
201C4×C43—82no—
202C4×C43—81no—
203Dic43—42no—
204Dic43—81no—
205Dic43—82no—
206Dic43—81no—
207Dic43—81no—
208Dic43—81no—
209Dic43—81no—
210#2804—431no—
211#1867—431no—
212#1867—431no—
213#1856—431no—
214#1393—431no—
215#1390—431no—
216#1390D4311yescharacteristic
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—41no—
220C2×C43—41no—
221C2×C43—41no—
222C2×C43—41no—
223C2×C43#206211yescharacteristic
224C2×C43#219811yescharacteristic
225C2×C43#219911yescharacteristic
226#518—431no—
227#428—861no—
228C2×#100C2×D4311yescharacteristic
229C2×#99—431no—
230C2×#99C2×D4311yescharacteristic
231#400—861no—
232#393—861no—
233#393—861no—
234#391—861no—
235#390—431no—
236#386—431no—
237#386C2×D4311yescharacteristic
238#385—861no—
239#385—861no—
240#385—861no—
241#385—861no—
242#342—861no—
243#342—861no—
244#339—861no—
245C43#1346311yescharacteristic, complemented, Sylow
246C22×Q8—861no—
247C22×D4C22×D4311yescharacteristic
248C23×C4—431no—
249C23×C4D17211yescharacteristic
250C2×M16—21no—
251C4×D4—1721no—
252C4×D4—1721no—
253#117—861no—
254C2×C4⋊C4—431no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4—861no—
257C2×C4⋊C4—1721no—
258C2×C4⋊C4—1721no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—431no—
262C2×C22⋊C4—861no—
263C2×C22⋊C4—861no—
264C2×C22⋊C4—861no—
265C2×C22⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C22⋊C4—861no—
268C2×C22⋊C4D17211yescharacteristic
269C2×C42—431no—
270#107—1721no—
271#106—1721no—
272#100—21no—
273#100Dic8612yescomplemented
274#99—21no—
275#99—432no—
276#99—861no—
277#99Dic8612yescomplemented
278#95—21no—
279#95—861no—
280#95—861no—
281#95—861no—
282#95—861no—
283#95—861no—
284#95—861no—
285#95—1721no—
286#95—1721no—
287C24C2×D17211yescharacteristic
288C24D4×D4311yescharacteristic
289C2×Q8—3441no—
290C2×Q8—3441no—
291C2×Q8—1722no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4C2×Dic8611yescharacteristic
295C2×D4C2×Dic8611yescharacteristic
296C2×D4#1062190011yescharacteristic
297C2×D4Q8×D4311yescharacteristic
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—81no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4—861no—
306C22×C4—861no—
307C22×C4—861no—
308C22×C4—861no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—3441no—
312C22×C4—1721no—
313C22×C4—1721no—
314C22×C4D4×D4311yescharacteristic
315M16—22no—
316M16—41no—
317C2×C8—41no—
318C4⋊C4—861no—
319C4⋊C4—861no—
320C4⋊C4—3442no—
321C4⋊C4—3441no—
322C4⋊C4—3441no—
323C4⋊C4—3442no—
324C4⋊C4—1721no—
325C22⋊C4—22no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—81no—
329C22⋊C4—862no—
330C22⋊C4—3441no—
331C22⋊C4—1722no—
332C22⋊C4—1722no—
333C22⋊C4—1721no—
334C22⋊C4—1721no—
335C22⋊C4—1721no—
336C22⋊C4—1721no—
337C22⋊C4—1721no—
338C42—1721no—
339C42—1721no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23#1306329511yescharacteristic
349C23#1306330211yescharacteristic
350C23#1306330511yescharacteristic
351C23#1306332411yescharacteristic
352C23#1306332511yescharacteristic
353Q8—3444no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—41no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—862no—
372C2×C4—3441no—
373C2×C4—3441no—
374C2×C4—3441no—
375C2×C4—3441no—
376C2×C4—3441no—
377C2×C4—3441no—
378C2×C4—3441no—
379C2×C4—1722no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4—1721no—
386C2×C4—1722no—
387C2×C4—1721no—
388C2×C4—1721no—
389C2×C4—1721no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4—1721no—
393C2×C4—1721no—
394C2×C4#1306330211yescharacteristic
395C2×C4#1306332411yescharacteristic
396C8—42no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22#1458282011yescharacteristic
414C22#1458308711yescharacteristic
415C22#1458309011yescharacteristic
416C4—21no—
417C4—21no—
418C4—81no—
419C4—82no—
420C4—81no—
421C4—3441no—
422C4—3442no—
423C4—3441no—
424C4—3441no—
425C4—3441no—
426C4—3441no—
427C4—1722no—
428C2—21no—
429C2—21no—
430C2—41no—
431C2—41no—
432C2—41no—
433C2—41no—
434C2#1913594911yescharacteristic
435C2#1913659211yescharacteristic
436C2#1913659711yescharacteristic
subgroupG/H
centerC22#14583087
commutator, prime radical, cosocleC22×D4×C43C23
FrattiniC22×D4C22×D43
FittingC43×#1390C2
socleC22×C43B(4,𝔽2)
hypercenter#1390D43
hypocenterC43#13463
LCSG ▷ C22×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1390

Complements

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

NH ≅ G/Ntype
48. #13063240Q8semidirect
64. #100×C43Q8semidirect
66. #99×C43Q8semidirect
245. C43#13463semidirect
273. #100Dic86semidirect
277. #99Dic86semidirect

Maximal subgroups

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

subgroupindex
#191425382
#191348782
#191348752
#191348072
#191327192
#191327142
C43×#13902
#1346343