Finite Group Databasebeta

← #24991685

Subgroups — #24991685

Order 11008.

528 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143157C211yesmaximal, characteristic
2#19137867C211yesmaximal, characteristic
3#19133025C211yesmaximal, characteristic, complemented
4#19133023C211yesmaximal, characteristic, complemented
5#19132907C211yesmaximal, characteristic
6#19132498C211yesmaximal, characteristic, complemented
7C43×#1303C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×C4×Dic86C2211yescharacteristic
10C2×#13063282C2211yescharacteristic
11#14582952C2211yescharacteristic
12#14582924—22no—
13#14582924—22no—
14#14582923C2211yescharacteristic
15#14582922—21no—
16#14582839C411yescharacteristic
17#14582836C411yescharacteristic
18#14582829—21no—
19#14582821—21no—
20#14582820C411yescharacteristic
21#14582812C411yescharacteristic
22C4×C4⋊Dic43—21no—
23C4×(C2×D43)⋊C4—21no—
24#14582631—22no—
25#14582629—22no—
26#14582624—21no—
27#14582622—21no—
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C4×C4⋊C4×C43C2211yescharacteristic
31C22×Dic86C2×C411yescharacteristic
32C22×C4×D43D411yescharacteristic
33C2×#10621877—21no—
34C2×#10621872—22no—
35M16×D43—42no—
36M16×D43—42no—
37C2×C8×D43—22no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40C4×Dic86—21no—
41C4×Dic86—21no—
42#13063282—21no—
43#13063282—21no—
44#13063282—21no—
45#13063282—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×Dic43⋊C4—21no—
50C2×Dic43⋊C4C2×C411yescharacteristic
51C2×Dic43⋊C4D411yescharacteristic
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4C2×C411yescharacteristic
55C2×(C2×D43)⋊C4D411yescharacteristic
56C2×C4×Dic43—21no—
57C2×C4×Dic43D411yescharacteristic
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)—21no—
60C4⋊(C43⋊C8)D412yes—
61Dic43⋊C8—24no—
62C22⋊(C43⋊C8)—21no—
63C4×C43⋊C8—21no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C43⋊#95—21no—
68C2×M16×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C42×C43—21no—
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—21no—
73C4⋊C8×C43—21no—
74C4⋊C8×C43D412yes—
75C22⋊C8×C43—21no—
76C4×C8×C43—21no—
77#95×C43C2×C411yescharacteristic
78#95×C43C2×C411yescharacteristic
79C23×D43C22⋊C411yescharacteristic
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43C22×C411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43C22⋊C411yescharacteristic
88C22×Dic43C22⋊C411yescharacteristic
89C22×Dic43C22⋊C411yescharacteristic
90C2×C4×D43—21no—
91C2×C4×D43—21no—
92C2×C4×D43—21no—
93C2×C4×D43—21no—
94C2×C4×D43SD1612yes—
95C2×C4×D43Q1612yes—
96C2×Dic86—21no—
97C2×Dic86—21no—
98C2×Dic86—42no—
99M16×C43—41no—
100M16×C43—41no—
101C2×C8×C43—22no—
102C2×C8×C43—41no—
103C4⋊C4×C43—42no—
104C42×C43—41no—
105C42×C43—41no—
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43#4111yescharacteristic
109C42×C43#4111yescharacteristic
110(C2×D43)⋊C4—21no—
111(C2×D43)⋊C4—21no—
112(C2×D43)⋊C4—21no—
113(C2×D43)⋊C4—21no—
114(C2×D43)⋊C4—42no—
115(C2×D43)⋊C4—42no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—42no—
119C4⋊Dic43—42no—
120Dic43⋊C4—21no—
121Dic43⋊C4—21no—
122Dic43⋊C4—21no—
123Dic43⋊C4—21no—
124Dic43⋊C4—41no—
125Dic43⋊C4—41no—
126C4×Dic43—21no—
127C4×Dic43—21no—
128C4×Dic43—41no—
129C4×Dic43—41no—
130#10621877—41no—
131#10621877—41no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—41no—
134#10621872—44no—
135C8×D43—44no—
136C23×C43C2×C22⋊C411yescharacteristic
137C22×D43—21no—
138C22×D43—21no—
139C22×D43—41no—
140C22×D43—41no—
141C22×D43#10312yes—
142C2×C4×C43—22no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43C4×D411yescharacteristic
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43#12011yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12311yescharacteristic
156C2×C4×C43C2×SD1611yescharacteristic
157C2×C4×C43C2×Q1611yescharacteristic
158C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C43#13711yescharacteristic
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—22no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43#10312yes—
173C4×D43—22no—
174C4×D43—22no—
175C4×D43—22no—
176C4×D43—22no—
177Dic86—22no—
178Dic86—22no—
179Dic86—41no—
180Dic86—41no—
181C8×C43—42no—
182C8×C43—81no—
183C43⋊C8—42no—
184C43⋊C8—81no—
185#9033—431nomaximal, Sylow
186C22×C43—21no—
187C22×C43—21no—
188C22×C43#38611yescharacteristic
189C22×C43C2×#10311yescharacteristic
190C22×C43#41711yescharacteristic
191C2×D43—22no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—42no—
195C2×D43—81no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—42no—
201C4×C43—81no—
202C4×C43#45011yescharacteristic
203C4×C43#45111yescharacteristic
204C4×C43#48311yescharacteristic
205C4×C43#48411yescharacteristic
206Dic43—22no—
207Dic43—41no—
208Dic43—42no—
209Dic43—41no—
210Dic43—81no—
211#2905—431no—
212#2396—431no—
213#1487—431no—
214#1487—431no—
215#1458—431no—
216#1303—431no—
217#1303D4311yescharacteristic, complemented
218C2×C43—21no—
219C2×C43—21no—
220C2×C43#187211yescharacteristic
221C2×C43#188411yescharacteristic
222C2×C43#189111yescharacteristic
223D43—42no—
224C22×M16—861no—
225C2×C4×Q8—431no—
226C2×#117—431no—
227#431—431no—
228#431C2×D4311yescharacteristic
229#424—862no—
230#424—862no—
231#423—431no—
232#423—861no—
233#423C2×D4311yescharacteristic
234#400—431no—
235#399—431no—
236#398—861no—
237#396—861no—
238#395—431no—
239#393—431no—
240C4×C4⋊C4—861no—
241C4×C4⋊C4C2×D4311yescharacteristic
242C4×C22⋊C4—861no—
243Q8⋊C8—862no—
244Q8⋊C8—862no—
245#324—861no—
246#323—861no—
247C43#903311yescharacteristic, complemented, Sylow
248C22×Q8—431no—
249C23×C4—431no—
250C2×M16—21no—
251C2×M16—862no—
252C2×M16—861no—
253C2×M16—1722no—
254C2×M16—1722no—
255C22×C8—862no—
256C4×Q8—861no—
257C4×Q8—861no—
258C4×Q8—861no—
259C4×Q8—861no—
260#117—861no—
261#117—861no—
262#117—861no—
263#117—861no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—431no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4—431no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4—861no—
270C2×C4⋊C4—861no—
271C2×C22⋊C4—431no—
272C2×C22⋊C4—431no—
273C2×C22⋊C4—861no—
274C2×C22⋊C4—861no—
275C2×C42—21no—
276C2×C42—431no—
277C2×C42—861no—
278C2×C42C22×D4311yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—432no—
282C4⋊C8—864no—
283C4⋊C8—861no—
284C4⋊C8—861no—
285C4⋊C8D17212yes—
286C22⋊C8—21no—
287C22⋊C8—861no—
288C4×C8—21no—
289C4×C8—861no—
290#95—861no—
291#95—861no—
292#95—861no—
293#95—861no—
294#95C4×D4311yescharacteristic
295#95C4×D4311yescharacteristic
296C24—431no—
297C2×Q8—861no—
298C2×Q8—861no—
299C2×Q8—1722no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—431no—
303C22×C4—432no—
304C22×C4—432no—
305C22×C4—431no—
306C22×C4—431no—
307C22×C4—861no—
308C22×C4—861no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4C2×C4×D4311yescharacteristic
314C22×C4D4×D4311yescharacteristic
315C22×C4D4×D4311yescharacteristic
316M16—41no—
317M16—41no—
318M16—1724no—
319M16—1721no—
320M16—1721no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—862no—
324C2×C8—1724no—
325C2×C8—1721no—
326C4⋊C4—42no—
327C4⋊C4—861no—
328C4⋊C4—861no—
329C4⋊C4—861no—
330C4⋊C4—861no—
331C4⋊C4—861no—
332C4⋊C4—861no—
333C4⋊C4—1722no—
334C4⋊C4—1722no—
335C4⋊C4—1721no—
336C4⋊C4—1721no—
337C22⋊C4—861no—
338C22⋊C4—861no—
339C22⋊C4—861no—
340C22⋊C4—861no—
341C22⋊C4—1722no—
342C22⋊C4—1722no—
343C42—41no—
344C42—41no—
345C42—861no—
346C42—861no—
347C42—1721no—
348C42—1721no—
349C42C2×D17211yescharacteristic
350C42#1062189811yescharacteristic
351C42D4×D4311yescharacteristic
352C42#1062190211yescharacteristic
353C23—432no—
354C23—861no—
355C23—861no—
356C23—1721no—
357C23—1721no—
358C23C22⋊C4×D4311yescharacteristic
359Q8—862no—
360Q8—862no—
361Q8—1721no—
362Q8—1721no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—432no—
372C2×C4—861no—
373C2×C4—861no—
374C2×C4—862no—
375C2×C4—862no—
376C2×C4—862no—
377C2×C4—862no—
378C2×C4—862no—
379C2×C4—861no—
380C2×C4—861no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4—1721no—
386C2×C4—1721no—
387C2×C4—1721no—
388C2×C4#1306328711yescharacteristic
389C2×C4C4×D17211yescharacteristic
390C2×C4#1306329511yescharacteristic
391C2×C4#1306329811yescharacteristic
392C2×C4#1306330011yescharacteristic
393C2×C4#1306331011yescharacteristic
394C2×C4SD16×D4311yescharacteristic
395C2×C4Q16×D4311yescharacteristic
396C2×C4#1306334911yescharacteristic
397C2×C4#1306335411yescharacteristic
398C8—42no—
399C8—81no—
400C8—3441no—
401C8—1722no—
402C22—21no—
403C22—21no—
404C22—862no—
405C22—3441no—
406C22—1722no—
407C22—1721no—
408C22—1721no—
409C22#1458277711yescharacteristic
410C22#103×D4311yescharacteristic
411C22#1458289711yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—862no—
419C4—3441no—
420C4—1721no—
421C4—1722no—
422C4—1721no—
423C4#1458305111yescharacteristic
424C4#1458305611yescharacteristic
425C4#1458323111yescharacteristic
426C4#1458323611yescharacteristic
427C2—21no—
428C2—21no—
429C2—1722no—
430C2#1913490111yescharacteristic
431C2#1913497711yescharacteristic
432C2#1913501211yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1303C2
socleC22×C43#386
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1303D43
hypocenterC43#9033
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #19133025C2semidirect
4. #19133023C2semidirect
6. #19132498C2semidirect
7. C43×#1303C2semidirect
217. #1303D43semidirect
247. C43#9033semidirect

Maximal subgroups

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

subgroupindex
#191431572
#191378672
#191330252
#191330232
#191329072
#191324982
C43×#13032
#903343