Finite Group Databasebeta

← #24992204

Subgroups — #24992204

Order 11008.

614 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582851C211yesmaximal, characteristic
2#19142900C211yesmaximal, characteristic
3#19134358C211yesmaximal, characteristic
4C2×#14582641C211yesmaximal, characteristic, complemented
5#19132477C211yesmaximal, characteristic, complemented
6#19132477C211yesmaximal, characteristic, complemented
7C2×C43×#330C211yesmaximal, characteristic, complemented
8C22×#10621872—21no—
9C2×C42×D43C2211yescharacteristic
10C2×(C2×D43)⋊C8—21no—
11#14582851—22no—
12#14582851—22no—
13C2×#13063236C2211yescharacteristic
14C2×#13063236C2211yescharacteristic
15C2×C8×Dic43—21no—
16#14582795C411yescharacteristic
17#14582795C411yescharacteristic
18#14582780—21no—
19#14582780—21no—
20#14582770—21no—
21#14582770—21no—
22#14582765C2211yescharacteristic
23#14582756C411yescharacteristic
24#14582756C411yescharacteristic
25#14582653—21no—
26#14582641—22no—
27C2×#125×C43C2211yescharacteristic
28C2×#97×C43C2211yescharacteristic
29C2×#97×C43C2211yescharacteristic
30C43×#330—22no—
31C22×C4×D43C2×C411yescharacteristic
32C22×C4×D43D411yescharacteristic
33C22×C4×D43D411yescharacteristic
34C2×#10621872—24no—
35C2×#10621872—24no—
36C2×#10621872—24no—
37C22×C43⋊C8—21no—
38C22×C43⋊C8—21no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43C2×C411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×C4×Dic43C2×C411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47C2×C4×Dic43D411yescharacteristic
48C42×D43—21no—
49C42×D43—21no—
50C42×D43—21no—
51C42×D43—21no—
52(C2×D43)⋊C8—24no—
53#13063236—21no—
54#13063236—21no—
55#13063236—21no—
56#13063236D412yes—
57C8×Dic43—24no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C22×C8×C43—21no—
65C22×C8×C43—21no—
66#125×C43—21no—
67#125×C43—21no—
68#125×C43—21no—
69#125×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43C2×C411yescharacteristic
73C2×C4⋊C4×C43C2×C411yescharacteristic
74C2×C42×C43C2311yescharacteristic
75#97×C43—21no—
76#97×C43—21no—
77#97×C43—21no—
78#97×C43D412yes—
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—22no—
93C2×C4×D43—21no—
94C2×C4×D43—21no—
95C2×C4×D43—21no—
96C2×C4×D43—21no—
97C2×C4×D43—22no—
98C2×C4×D43—22no—
99C2×C4×D43—22no—
100C2×C4×D43—41no—
101C2×C4×D43—41no—
102C2×C8×C43—22no—
103C2×C8×C43—22no—
104C2×C8×C43—22no—
105C2×C8×C43—22no—
106C2×C8×C43—41no—
107C2×C8×C43—41no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—41no—
116C42×C43C2×D411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43#4111yescharacteristic
119C42×C43#4111yescharacteristic
120(C2×D43)⋊C4—42no—
121(C2×D43)⋊C4—42no—
122C4⋊Dic43—41no—
123C4⋊Dic43—41no—
124Dic43⋊C4—42no—
125Dic43⋊C4—42no—
126C4×Dic43—21no—
127C4×Dic43—21no—
128C4×Dic43—21no—
129C4×Dic43—21no—
130C4×Dic43—21no—
131C4×Dic43—21no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—22no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8—22no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—41no—
138#10621872—216no—
139C23×C43C2×C22⋊C411yescharacteristic
140C22×D43—21no—
141C22×D43—21no—
142C22×D43—21no—
143C22×D43—21no—
144C22×D43—21no—
145C22×D43—21no—
146C22×D43#10412yes—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43C4×D411yescharacteristic
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43#12011yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#12311yescharacteristic
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43#10112yes—
178C2×Dic43#10412yes—
179C2×Dic43#10412yes—
180C4×D43—24no—
181C4×D43—24no—
182C4×D43—42no—
183C4×D43—42no—
184C4×D43—42no—
185C4×D43—42no—
186C8×C43—24no—
187C8×C43—42no—
188C43⋊C8—24no—
189C43⋊C8—42no—
190#9122—431nomaximal, Sylow
191C22×C43#38611yescharacteristic
192C22×C43C2×#10111yescharacteristic
193C22×C43#41311yescharacteristic
194C22×C43C2×#10411yescharacteristic
195C22×C43C2×#10411yescharacteristic
196C22×C43C2×#10411yescharacteristic
197C22×C43#42111yescharacteristic
198C2×D43—22no—
199C2×D43—22no—
200C2×D43—22no—
201C2×D43—41no—
202C2×D43—41no—
203C2×D43—41no—
204C2×D43—41no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—81no—
212C4×C43—81no—
213Dic43—22no—
214Dic43—22no—
215Dic43—22no—
216Dic43—81no—
217Dic43—81no—
218C2×C4×M16—431no—
219#2851—431no—
220#1749—431no—
221C2×#330—431no—
222C2×#330D4311yescharacteristic, complemented
223#1295—431no—
224#1295—431no—
225C2×C43#152411yescharacteristic
226C2×C43#152611yescharacteristic
227C2×C43#152811yescharacteristic
228C2×C43#152911yescharacteristic
229C2×C43#187111yescharacteristic
230C2×C43#189611yescharacteristic
231C2×C43#190111yescharacteristic
232D43—42no—
233C22×M16—861no—
234C2×#125C2×D4311yescharacteristic
235C22×C42—431no—
236C2×C22⋊C8—861no—
237C4×M16—862no—
238C4×M16—862no—
239C2×#97—431no—
240C2×#97—431no—
241C2×#97C2×D4311yescharacteristic
242C2×#97C2×D4311yescharacteristic
243C2×C4×C8—861no—
244#389—431no—
245#389—431no—
246#387—861no—
247#387—861no—
248#385—861no—
249#385—861no—
250#382—431no—
251#380—431no—
252#380—431no—
253#336—861no—
254#330—22no—
255#330—862no—
256C43#912211yescharacteristic, complemented, Sylow
257C23×C4—431no—
258C23×C4—431no—
259C23×C4—431no—
260C2×M16—864no—
261C2×M16—864no—
262C2×M16—864no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—861no—
266C22×C8—861no—
267#125—21no—
268#125—21no—
269#125—21no—
270#125—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—431no—
274C2×C4⋊C4—431no—
275C2×C4⋊C4—861no—
276C2×C4⋊C4—861no—
277C2×C4⋊C4C4×D4311yescharacteristic
278C2×C4⋊C4C4×D4311yescharacteristic
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C42—431no—
282C2×C42—431no—
283C2×C42—431no—
284C2×C42—861no—
285C2×C42—861no—
286C2×C42—861no—
287C2×C42—861no—
288C2×C42C22×D4311yescharacteristic
289C22⋊C8—864no—
290#97—21no—
291#97—21no—
292#97—21no—
293#97—432no—
294#97—861no—
295#97—861no—
296#97—861no—
297#97C22⋊D4312yes—
298C4×C8—864no—
299#95—861no—
300#95—861no—
301#95—861no—
302#95—861no—
303#95—861no—
304#95—861no—
305C24—431no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—431no—
309C22×C4—431no—
310C22×C4—431no—
311C22×C4—862no—
312C22×C4—862no—
313C22×C4—862no—
314C22×C4—862no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4—1721no—
324C22×C4—1721no—
325C22×C4C2×C4×D4311yescharacteristic
326C22×C4D4×D4311yescharacteristic
327C22×C4D4×D4311yescharacteristic
328M16—8616no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—862no—
336C2×C8—862no—
337C2×C8—862no—
338C2×C8—862no—
339C2×C8—1721no—
340C2×C8—1721no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—1721no—
350C4⋊C4—1721no—
351C4⋊C4—1722no—
352C4⋊C4—1722no—
353C22⋊C4—1722no—
354C22⋊C4—1722no—
355C42—861no—
356C42—861no—
357C42—861no—
358C42—861no—
359C42—861no—
360C42—861no—
361C42#1062189811yescharacteristic
362C42D4×D4311yescharacteristic
363C42#1062190011yescharacteristic
364C42C2×C22⋊D4311yescharacteristic
365C23—432no—
366C23—861no—
367C23—861no—
368C23—861no—
369C23—861no—
370C23—861no—
371C23—861no—
372C23C22⋊C4×D4311yescharacteristic
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—432no—
386C2×C4—432no—
387C2×C4—432no—
388C2×C4—864no—
389C2×C4—864no—
390C2×C4—861no—
391C2×C4—861no—
392C2×C4—861no—
393C2×C4—861no—
394C2×C4—861no—
395C2×C4—861no—
396C2×C4—1722no—
397C2×C4—1722no—
398C2×C4—1722no—
399C2×C4—1722no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4—1721no—
406C2×C4(C22⋊D43)⋊C411yescharacteristic
407C2×C4C4×C22⋊D4311yescharacteristic
408C2×C4#1306329311yescharacteristic
409C2×C4#1306329611yescharacteristic
410C2×C4#1306329811yescharacteristic
411C2×C4#1306330711yescharacteristic
412C8—24no—
413C8—42no—
414C8—864no—
415C8—1722no—
416C22—862no—
417C22—862no—
418C22—862no—
419C22—1721no—
420C22—1721no—
421C22—1721no—
422C22—1721no—
423C22#1458277511yescharacteristic
424C22#101×D4311yescharacteristic
425C22#1458288211yescharacteristic
426C22#104×D4311yescharacteristic
427C22#104×D4311yescharacteristic
428C22#104×D4311yescharacteristic
429C22#1458291411yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—862no—
439C4—862no—
440C4—862no—
441C4—3441no—
442C4—3441no—
443C2—1722no—
444C2#1913318211yescharacteristic
445C2#1913318811yescharacteristic
446C2#1913319511yescharacteristic
447C2#1913320111yescharacteristic
448C2#1913489411yescharacteristic
449C2#1913503511yescharacteristic
450C2#1913506011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#330C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenterC2×#330D43
hypocenterC43#9122
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
4. C2×#14582641C2semidirect
5. #19132477C2semidirect
6. #19132477C2semidirect
7. C2×C43×#330C2semidirect
222. C2×#330D43semidirect
256. C43#9122semidirect

Maximal subgroups

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

subgroupindex
C2×#145828512
#191429002
#191343582
C2×#145826412
#191324772
C2×C43×#3302
#912243