Finite Group Databasebeta

← #24991638

Subgroups — #24991638

Order 11008.

740 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582834C211yesmaximal, characteristic
2#19137192C211yesmaximal, characteristic
3#19134685C211yesmaximal, characteristic, complemented
4C2×#14582622C211yesmaximal, characteristic
5#19132475C211yesmaximal, characteristic, complemented
6#19132473C211yesmaximal, characteristic, complemented
7C43×#1824C211yesmaximal, characteristic, complemented
8C22×Dic43⋊C4—21no—
9C22×(C2×D43)⋊C4—21no—
10C22×(C2×D43)⋊C4C2211yescharacteristic
11C2×C22⋊(C43⋊C8)C2211yescharacteristic
12#14582834—22no—
13#14582834C414yescomplemented
14#14582791—22no—
15#14582789—22no—
16#14582759C2211yescharacteristic
17#14582754—21no—
18C22⋊C4×Dic43—21no—
19C2×C43⋊#95C2211yescharacteristic
20#14582661—22no—
21#14582622—22no—
22C22×C4⋊C4×C43C2211yescharacteristic
23C2×C22⋊C8×C43C2211yescharacteristic
24C43×#380C2211yescharacteristic
25C43×#340—22no—
26C24×D43D411yescharacteristic
27C23×Dic43—21no—
28C23×Dic43D411yescharacteristic
29C22×C43⋊C8—21no—
30C2×C4⋊Dic43D412yes—
31C2×Dic43⋊C4—24no—
32C2×Dic43⋊C4—44no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—24no—
39C2×(C2×D43)⋊C4—22no—
40C2×(C2×D43)⋊C4—22no—
41C2×(C2×D43)⋊C4—44no—
42C2×(C2×D43)⋊C4C2×C412yes—
43C2×(C2×D43)⋊C4D412yes—
44C2×C4×Dic43—22no—
45C22⋊(C43⋊C8)—21no—
46C22⋊(C43⋊C8)—21no—
47C43⋊#95—22no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95C2×C412yes—
51C23×C4×C43—21no—
52C23×C4×C43C2311yescharacteristic
53C22×C8×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43C2×C412yes—
60C2×C4⋊C4×C43D412yes—
61C2×C22⋊C4×C43—21no—
62C22⋊C8×C43—21no—
63C22⋊C8×C43—21no—
64#95×C43—21no—
65C24×C43C2×D411yescharacteristic
66C23×D43—21no—
67C23×D43—21no—
68C23×D43—21no—
69C23×D43—21no—
70C23×D43—21no—
71C23×D43—21no—
72C23×D43—42no—
73C23×D43—42no—
74C23×D43C22⋊C412yes—
75C22×C4×C43—22no—
76C22×C4×C43—22no—
77C22×C4×C43—42no—
78C22×C4×C43—42no—
79C22×C4×C43—42no—
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43C22×C411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C22×Dic43—24no—
89C22×Dic43—22no—
90C22×Dic43—21no—
91C22×Dic43—22no—
92C22×Dic43—21no—
93C22×Dic43—42no—
94C22×Dic43—42no—
95C22×Dic43—41no—
96C22×Dic43—41no—
97C22×Dic43C22⋊C412yes—
98C2×C8×C43—42no—
99C2×C8×C43—41no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—42no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C22⋊Dic43—41no—
108C22⋊Dic43—41no—
109(C2×D43)⋊C4—22no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4—22no—
112(C2×D43)⋊C4—22no—
113(C2×D43)⋊C4—48no—
114(C2×D43)⋊C4—82no—
115(C2×D43)⋊C4—82no—
116C4⋊Dic43—42no—
117Dic43⋊C4—48no—
118C4×Dic43—82no—
119C2×C43⋊C8—42no—
120C2×C43⋊C8—41no—
121C23×C43—22no—
122C23×C43—22no—
123C23×C43C2×C22⋊C411yescharacteristic
124C23×C43#12011yescharacteristic
125C23×C43#12311yescharacteristic
126C23×C43#13511yescharacteristic
127C23×C43#13511yescharacteristic
128C23×C43#13711yescharacteristic
129C23×C43#13711yescharacteristic
130C22×D43—22no—
131C22×D43—22no—
132C22×D43—22no—
133C22×D43—42no—
134C22×D43—42no—
135C22×D43—44no—
136C22×D43—44no—
137C22×D43—41no—
138C22×D43—41no—
139C22×D43—42no—
140C22×D43—42no—
141C22×D43—41no—
142C22×D43—41no—
143C22×D43—81no—
144C22×D43—81no—
145C22×D43—82no—
146C22×D43—82no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—82no—
160C2×C4×C43—82no—
161C2×C4×C43C4×D411yescharacteristic
162C2×C4×C43C4×D411yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×Dic43—24no—
166C2×Dic43—22no—
167C2×Dic43—44no—
168C2×Dic43—44no—
169C2×Dic43—42no—
170C2×Dic43—42no—
171C2×Dic43—42no—
172C2×Dic43—42no—
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—81no—
177C8×C43—81no—
178C43⋊C8—81no—
179#9024—431nomaximal, Sylow
180C22×C43—22no—
181C22×C43—22no—
182C22×C43—22no—
183C22×C43—22no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43#38611yescharacteristic
189C22×C43#41611yescharacteristic
190C22×C43#41911yescharacteristic
191C22×C43#45211yescharacteristic
192C22×C43#45211yescharacteristic
193C22×C43#45312yes—
194C22×C43#45812yes—
195C22×C43#48511yescharacteristic
196C22×C43#48511yescharacteristic
197C2×D43—44no—
198C2×D43—42no—
199C2×D43—42no—
200C2×D43—42no—
201C2×D43—82no—
202C2×D43—82no—
203C2×D43—82no—
204C2×D43—82no—
205C2×D43—82no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—82no—
211C4×C43—82no—
212Dic43—44no—
213Dic43—42no—
214Dic43—82no—
215C2×#399—431no—
216#2312—431no—
217#1824—431no—
218#1824D4311yescharacteristic, complemented
219C2×#323—431no—
220#1294—431no—
221#1294—431no—
222C2×C43—21no—
223C2×C43—21no—
224C2×C43—21no—
225C2×C43—21no—
226C2×C43#161812yes—
227C2×C43#161812yes—
228C2×C43#187311yescharacteristic
229C2×C43#188711yescharacteristic
230C2×C43#189011yescharacteristic
231D43—82no—
232C22×C4⋊C4—861no—
233C22×C4⋊C4C2×D4311yescharacteristic
234C22×C22⋊C4—431no—
235C22×C22⋊C4—861no—
236C2×C22⋊C8—431no—
237C2×C22⋊C8C2×D4311yescharacteristic
238#399—434no—
239#399—862no—
240#388—862no—
241#388—862no—
242#380—431no—
243#380C2×D4311yescharacteristic
244#379—861no—
245C4×C22⋊C4—861no—
246C2×#95—431no—
247#340—22no—
248#340—862no—
249#323—862no—
250C43#902411yescharacteristic, complemented, Sylow
251C25—431no—
252C23×C4—21no—
253C23×C4—431no—
254C23×C4—861no—
255C23×C4C22×D4311yescharacteristic
256C22×C8—21no—
257C22×C8—861no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—432no—
264C2×C4⋊C4—864no—
265C2×C4⋊C4—1724no—
266C2×C4⋊C4C4×D4312yes—
267C2×C4⋊C4C22⋊D4312yes—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—432no—
270C2×C22⋊C4—432no—
271C2×C22⋊C4—861no—
272C2×C22⋊C4—861no—
273C2×C22⋊C4—861no—
274C2×C22⋊C4—861no—
275C2×C22⋊C4—862no—
276C2×C22⋊C4—862no—
277C2×C22⋊C4—864no—
278C2×C22⋊C4—861no—
279C2×C22⋊C4—1724no—
280C2×C42—862no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—861no—
284C22⋊C8—861no—
285#95—21no—
286#95—432no—
287#95—862no—
288#95—861no—
289#95—861no—
290C24—432no—
291C24—861no—
292C24—861no—
293C24—861no—
294C24—861no—
295C24—861no—
296C24—861no—
297C24—1722no—
298C24—1722no—
299C24D4×D4311yescharacteristic
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—432no—
308C22×C4—861no—
309C22×C4—864no—
310C22×C4—862no—
311C22×C4—861no—
312C22×C4—862no—
313C22×C4—1722no—
314C22×C4—1722no—
315C22×C4—1721no—
316C22×C4—1721no—
317C22×C4C2×C4×D4311yescharacteristic
318C22×C4#1062189811yescharacteristic
319C22×C4D4×D4311yescharacteristic
320C22×C4D4×D4311yescharacteristic
321C22×C4#1062190011yescharacteristic
322C22×C4C2×C22⋊D4311yescharacteristic
323C2×C8—42no—
324C2×C8—41no—
325C2×C8—1722no—
326C2×C8—1721no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—42no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—1722no—
333C4⋊C4—1728no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—862no—
337C22⋊C4—862no—
338C22⋊C4—862no—
339C22⋊C4—862no—
340C22⋊C4—3442no—
341C22⋊C4—3442no—
342C22⋊C4—1728no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C42—3442no—
346C23—22no—
347C23—22no—
348C23—862no—
349C23—862no—
350C23—862no—
351C23—3442no—
352C23—3442no—
353C23—3441no—
354C23—3441no—
355C23—1724no—
356C23—1724no—
357C23—1722no—
358C23—1722no—
359C23—1721no—
360C23—1721no—
361C23—1722no—
362C23—1722no—
363C23—1721no—
364C23—1721no—
365C23C22⋊C4×D4311yescharacteristic
366C23#1306329311yescharacteristic
367C23#1306330711yescharacteristic
368C23#1306334611yescharacteristic
369C23#1306334811yescharacteristic
370C23#1306335411yescharacteristic
371C23#1306335711yescharacteristic
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—864no—
387C2×C4—862no—
388C2×C4—3441no—
389C2×C4—1722no—
390C2×C4—1722no—
391C2×C4—1722no—
392C2×C4—1722no—
393C2×C4—1724no—
394C2×C4—1724no—
395C2×C4—1722no—
396C2×C4—1722no—
397C2×C4—1722no—
398C2×C4(C22⋊D43)⋊C411yescharacteristic
399C2×C4C4×C22⋊D4311yescharacteristic
400C2×C4#1306329611yescharacteristic
401C2×C4#1306329811yescharacteristic
402C8—81no—
403C8—3441no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—3442no—
413C22—3442no—
414C22—3442no—
415C22—3442no—
416C22—3442no—
417C22—1724no—
418C22—1722no—
419C22—1722no—
420C22—1722no—
421C22#1458277511yescharacteristic
422C22#1458289411yescharacteristic
423C22#1458290611yescharacteristic
424C22#1458305811yescharacteristic
425C22#1458306011yescharacteristic
426C22#1458306512yes—
427C22#1458308812yes—
428C22#1458323811yescharacteristic
429C22#1458323911yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—82no—
435C4—82no—
436C4—3442no—
437C4—1724no—
438C4—1722no—
439C2—21no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—3442no—
444C2#1913364012yes—
445C2#1913364212yes—
446C2#1913490411yescharacteristic
447C2#1913499011yescharacteristic
448C2#1913500511yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1824C2
socleC23×C43#120
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1824D43
hypocenterC43#9024
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
3. #19134685C2semidirect
5. #19132475C2semidirect
6. #19132473C2semidirect
7. C43×#1824C2semidirect
13. #14582834C4semidirect
218. #1824D43semidirect
250. C43#9024semidirect

Maximal subgroups

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

subgroupindex
C2×#145828342
#191371922
#191346852
C2×#145826222
#191324752
#191324732
C43×#18242
#902443