Finite Group Databasebeta

← #24992219

Subgroups — #24992219

Order 11008.

530 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582954C211yesmaximal, characteristic
2#19142900C211yesmaximal, characteristic
3#19134358C211yesmaximal, characteristic
4C2×#14582641C211yesmaximal, characteristic, complemented
5#19132477C211yesmaximal, characteristic, complemented
6#19132477C211yesmaximal, characteristic, complemented
7C2×C43×#330C211yesmaximal, characteristic, complemented
8C2×C42×D43C2211yescharacteristic
9#14582954—22no—
10#14582954—22no—
11C2×Dic43⋊C8—21no—
12C2×(C2×D43)⋊C8—21no—
13C2×(C2×D43)⋊C8—21no—
14C2×#13063236C2211yescharacteristic
15C2×#13063236C2211yescharacteristic
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
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×C4×Dic43C2×C411yescharacteristic
43C2×C4×Dic43D411yescharacteristic
44C2×C4×Dic43D411yescharacteristic
45C42×D43—21no—
46C42×D43—21no—
47C42×D43—21no—
48C42×D43—21no—
49Dic43⋊C8—24no—
50(C2×D43)⋊C8—24no—
51(C2×D43)⋊C8—24no—
52#13063236—21no—
53#13063236—21no—
54#13063236—21no—
55#13063236D412yes—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C22×C8×C43—21no—
63C22×C8×C43—21no—
64#125×C43—21no—
65#125×C43—21no—
66#125×C43—21no—
67#125×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43C2×C411yescharacteristic
71C2×C4⋊C4×C43C2×C411yescharacteristic
72C2×C42×C43C2311yescharacteristic
73#97×C43—21no—
74#97×C43—21no—
75#97×C43—21no—
76#97×C43D412yes—
77C23×D43C22⋊C411yescharacteristic
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43C22×C411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43C22⋊C411yescharacteristic
86C22×Dic43C22⋊C411yescharacteristic
87C22×Dic43C22⋊C411yescharacteristic
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×C4×D43—21no—
91C2×C4×D43—21no—
92C2×C4×D43—21no—
93C2×C4×D43—21no—
94C2×C4×D43—22no—
95C2×C4×D43—22no—
96C2×C4×D43—41no—
97C2×C4×D43—41no—
98C2×C4×D43—41no—
99C2×C4×D43—41no—
100C2×C8×C43—22no—
101C2×C8×C43—22no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C42×C43C2×D411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43#4111yescharacteristic
117C42×C43#4111yescharacteristic
118(C2×D43)⋊C4—42no—
119(C2×D43)⋊C4—42no—
120C4⋊Dic43—41no—
121C4⋊Dic43—41no—
122Dic43⋊C4—42no—
123Dic43⋊C4—42no—
124C4×Dic43—21no—
125C4×Dic43—21no—
126C4×Dic43—21no—
127C4×Dic43—21no—
128C4×Dic43—21no—
129C4×Dic43—21no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—41no—
133C2×C43⋊C8—41no—
134C2×C43⋊C8—41no—
135C2×C43⋊C8—41no—
136C23×C43C2×C22⋊C411yescharacteristic
137C22×D43—21no—
138C22×D43—21no—
139C22×D43—21no—
140C22×D43—21no—
141C22×D43—21no—
142C22×D43—21no—
143C22×D43#10412yes—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43C4×D411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43#12011yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12311yescharacteristic
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43#10112yes—
177C4×D43—42no—
178C4×D43—42no—
179C4×D43—42no—
180C4×D43—42no—
181C4×D43—42no—
182C4×D43—42no—
183C8×C43—42no—
184C8×C43—42no—
185C43⋊C8—42no—
186C43⋊C8—42no—
187#9125—431nomaximal, Sylow
188C22×C43#38611yescharacteristic
189C22×C43C2×#10111yescharacteristic
190C22×C43#41311yescharacteristic
191C22×C43C2×#10411yescharacteristic
192C22×C43#42111yescharacteristic
193C22×C43#42111yescharacteristic
194C22×C43#42111yescharacteristic
195C2×D43—22no—
196C2×D43—22no—
197C2×D43—22no—
198C2×D43—41no—
199C2×D43—41no—
200C2×D43—41no—
201C2×D43—41no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—81no—
209C4×C43—81no—
210Dic43—22no—
211Dic43—41no—
212Dic43—41no—
213Dic43—81no—
214Dic43—81no—
215C2×#432—431no—
216#2851—431no—
217#1749—431no—
218C2×#330—431no—
219C2×#330D4311yescharacteristic, complemented
220#1295—431no—
221#1295—431no—
222C2×C43#152811yescharacteristic
223C2×C43#153211yescharacteristic
224C2×C43#153511yescharacteristic
225C2×C43#153711yescharacteristic
226C2×C43#187111yescharacteristic
227C2×C43#189711yescharacteristic
228C2×C43#190111yescharacteristic
229D43—42no—
230C2×#125C2×D4311yescharacteristic
231C22×C42—431no—
232#432—862no—
233#432—862no—
234C2×C4⋊C8—861no—
235C2×C22⋊C8—861no—
236C2×C22⋊C8—861no—
237C2×#97—431no—
238C2×#97—431no—
239C2×#97C2×D4311yescharacteristic
240C2×#97C2×D4311yescharacteristic
241#389—431no—
242#389—431no—
243#387—861no—
244#387—861no—
245#385—861no—
246#385—861no—
247#382—431no—
248#380—431no—
249#380—431no—
250#336—861no—
251#330—22no—
252#330—862no—
253C43#912511yescharacteristic, complemented, Sylow
254C23×C4—431no—
255C23×C4—431no—
256C23×C4—431no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—861no—
260C22×C8—861no—
261#125—21no—
262#125—21no—
263#125—21no—
264#125—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—431no—
268C2×C4⋊C4—431no—
269C2×C4⋊C4—861no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4C4×D4311yescharacteristic
272C2×C4⋊C4C4×D4311yescharacteristic
273C2×C22⋊C4—861no—
274C2×C22⋊C4—861no—
275C2×C42—431no—
276C2×C42—431no—
277C2×C42—431no—
278C2×C42—861no—
279C2×C42—861no—
280C2×C42—861no—
281C2×C42—861no—
282C2×C42C22×D4311yescharacteristic
283C4⋊C8—864no—
284C22⋊C8—864no—
285C22⋊C8—864no—
286#97—21no—
287#97—21no—
288#97—21no—
289#97—432no—
290#97—861no—
291#97—861no—
292#97—861no—
293#97C22⋊D4312yes—
294#95—861no—
295#95—861no—
296#95—861no—
297#95—861no—
298#95—861no—
299#95—861no—
300C24—431no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—431no—
304C22×C4—431no—
305C22×C4—431no—
306C22×C4—862no—
307C22×C4—862no—
308C22×C4—861no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—1721no—
317C22×C4—1721no—
318C22×C4—1721no—
319C22×C4—1721no—
320C22×C4C2×C4×D4311yescharacteristic
321C22×C4D4×D4311yescharacteristic
322C22×C4D4×D4311yescharacteristic
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—862no—
330C2×C8—862no—
331C2×C8—1721no—
332C2×C8—1721no—
333C2×C8—1721no—
334C2×C8—1721no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—1721no—
344C4⋊C4—1721no—
345C4⋊C4—1722no—
346C4⋊C4—1722no—
347C22⋊C4—1722no—
348C22⋊C4—1722no—
349C42—861no—
350C42—861no—
351C42—861no—
352C42—861no—
353C42—861no—
354C42—861no—
355C42#1062189811yescharacteristic
356C42D4×D4311yescharacteristic
357C42#1062190011yescharacteristic
358C42C2×C22⋊D4311yescharacteristic
359C23—432no—
360C23—861no—
361C23—861no—
362C23—861no—
363C23—861no—
364C23—861no—
365C23—861no—
366C23C22⋊C4×D4311yescharacteristic
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—432no—
380C2×C4—861no—
381C2×C4—861no—
382C2×C4—861no—
383C2×C4—861no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—861no—
388C2×C4—1722no—
389C2×C4—1722no—
390C2×C4—1722no—
391C2×C4—1722no—
392C2×C4—1722no—
393C2×C4—1722no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4(C22⋊D43)⋊C411yescharacteristic
401C2×C4C4×C22⋊D4311yescharacteristic
402C2×C4#1306329311yescharacteristic
403C2×C4#1306329611yescharacteristic
404C2×C4#1306329811yescharacteristic
405C2×C4#1306330711yescharacteristic
406C8—42no—
407C8—42no—
408C8—1722no—
409C8—1722no—
410C22—862no—
411C22—862no—
412C22—862no—
413C22—1721no—
414C22—1721no—
415C22—1721no—
416C22—1721no—
417C22#1458277511yescharacteristic
418C22#101×D4311yescharacteristic
419C22#1458288211yescharacteristic
420C22#104×D4311yescharacteristic
421C22#1458291411yescharacteristic
422C22#1458291411yescharacteristic
423C22#1458291411yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—81no—
431C4—81no—
432C4—862no—
433C4—3441no—
434C4—3441no—
435C4—1721no—
436C4—1721no—
437C2—1722no—
438C2#1913319511yescharacteristic
439C2#1913321411yescharacteristic
440C2#1913322511yescharacteristic
441C2#1913323111yescharacteristic
442C2#1913489411yescharacteristic
443C2#1913504011yescharacteristic
444C2#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#9125
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
219. C2×#330D43semidirect
253. C43#9125semidirect

Maximal subgroups

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

subgroupindex
C2×#145829542
#191429002
#191343582
C2×#145826412
#191324772
C2×C43×#3302
#912543