Finite Group Databasebeta

← #25014900

Subgroups — #25014900

Order 11008.

628 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 99 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#19139481C211yesmaximal, characteristic
2C2×#14582690C212yesmaximal, complemented
3C2×#14582687C212yesmaximal
4C4×#13063240C211yesmaximal, characteristic, complemented
5C43×#1800C211yesmaximal, characteristic, complemented
6C2×#13063306C2211yescharacteristic
7C2×#13063293C2211yescharacteristic
8C22×(C2×D43)⋊C4C411yescharacteristic, complemented
9C2×#13063240C2212yes—
10#14582821—21no—
11#14582815—21no—
12#14582790—21no—
13#14582778—21no—
14#14582760C411yescharacteristic, complemented
15#14582759C411yescharacteristic, complemented
16#14582754C411yescharacteristic, complemented
17C4×C22⋊Dic43—21no—
18#14582690—24no—
19#14582687—24no—
20#14582666—21no—
21C2×C4×D4×C43C2211yescharacteristic
22C43×#423—21no—
23C2×#100×C43C2212yes—
24C43×#343—21no—
25C24×D43C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C23×Dic43C2×C411yescharacteristic
28#13063306—22no—
29#13063306—22no—
30#13063293—22no—
31#13063293—22no—
32C2×C4⋊Dic43—21no—
33C2×Dic43⋊C4—21no—
34C2×C22⋊Dic43—22no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43C2×C411yescharacteristic
37C2×C22⋊Dic43C2×C411yescharacteristic
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—41no—
44C2×(C2×D43)⋊C4—41no—
45C2×C4×Dic43—41no—
46#13063240—22no—
47#13063240D414yes—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—41no—
52C22×D4×C43C2311yescharacteristic
53C23×C4×C43C2×C411yescharacteristic
54C23×C4×C43D411yescharacteristic
55C2×M16×C43—22no—
56C4×D4×C43—41no—
57C4×D4×C43—41no—
58C2×C4⋊C4×C43D411yescharacteristic
59C2×C22⋊C4×C43C2×C411yescharacteristic
60C2×C22⋊C4×C43D411yescharacteristic
61C2×C42×C43D411yescharacteristic
62C4⋊C8×C43—41no—
63C4⋊C8×C43—41no—
64#100×C43—22no—
65#100×C43—22no—
66C24×C43C22×C411yescharacteristic
67C24×C43C2×D411yescharacteristic
68C23×D43—21no—
69C23×D43—22no—
70C23×D43—42no—
71C23×D43—41no—
72C23×D43—41no—
73C23×D43—81no—
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C2×D4×C43C2×D412yes—
77C2×D4×C43#4112yes—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—81no—
83C22×C4×C43—81no—
84C22×C4×C43C22⋊C411yescharacteristic
85C22×C4×C43C22⋊C411yescharacteristic
86C22×C4×C43C22⋊C411yescharacteristic
87C22×C4×C43C22⋊C411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C2×C22⋊D43—42no—
90C2×C22⋊D43—42no—
91C2×C22⋊D43—81no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—22no—
96C22×Dic43—42no—
97C22×Dic43—41no—
98C22×Dic43—41no—
99M16×C43—42no—
100M16×C43—42no—
101C2×C8×C43—42no—
102C4⋊C4×C43—41no—
103C22⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C42×C43—21no—
106C42×C43—21no—
107C22⋊Dic43—22no—
108C22⋊Dic43—22no—
109C22⋊Dic43—24no—
110C22⋊Dic43—42no—
111C22⋊Dic43—42no—
112(C2×D43)⋊C4—42no—
113(C2×D43)⋊C4—42no—
114(C2×D43)⋊C4—41no—
115(C2×D43)⋊C4—41no—
116(C2×D43)⋊C4—41no—
117(C2×D43)⋊C4—41no—
118(C2×D43)⋊C4—81no—
119C4⋊Dic43—81no—
120Dic43⋊C4—41no—
121Dic43⋊C4—41no—
122C4×Dic43—82no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43C2×C22⋊C411yescharacteristic
132C23×C43C4×D412yes—
133C23×C43#12112yes—
134C22×D43—22no—
135C22×D43—41no—
136C22×D43—41no—
137C22×D43—41no—
138C22×D43—42no—
139C22×D43—41no—
140C22×D43—41no—
141C22×D43—41no—
142C22×D43—42no—
143C22×D43—84no—
144C22×D43—84no—
145C22×D43—82no—
146C22×D43—82no—
147D4×C43—42no—
148D4×C43—42no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—41no—
155C2×C4×C43—42no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43—81no—
162C2×C4×C43#9911yescharacteristic
163C2×C4×C43#9911yescharacteristic
164C2×C4×C43#12411yescharacteristic
165C2×C4×C43#12711yescharacteristic
166C22⋊D43—84no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—44no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—82no—
178C2×Dic43—82no—
179C2×Dic43—82no—
180C8×C43—82no—
181#13222—431nomaximal, Sylow
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—22no—
185C22×C43—22no—
186C22×C43—42no—
187C22×C43—42no—
188C22×C43—42no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—81no—
194C22×C43#39011yescharacteristic
195C22×C43C2×#9911yescharacteristic
196C22×C43#41011yescharacteristic
197C2×D43—42no—
198C2×D43—42no—
199C2×D43—42no—
200C2×D43—81no—
201C2×D43—81no—
202C2×D43—84no—
203C2×D43—81no—
204C2×D43—81no—
205C2×D43—84no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—41no—
211C4×C43—41no—
212C4×C43—41no—
213Dic43—81no—
214Dic43—81no—
215Dic43—84no—
216Dic43—81no—
217#2534—431no—
218C2×#352—432no—
219C2×AΣL(1,𝔽16)—432no—
220#1800D4311yescharacteristic, complemented
221C4×#99—431no—
222C2×C43—21no—
223C2×C43—21no—
224C2×C43—42no—
225C2×C43—42no—
226C2×C43#196411yescharacteristic
227C2×C43#212011yescharacteristic
228C2×C43#212111yescharacteristic
229D43—82no—
230C2×#123—431no—
231C2×#120—431no—
232C2×C4×D4C2×D4311yescharacteristic
233C22×C22⋊C4—431no—
234#423—21no—
235C2×#100C2×D4312yes—
236C2×#99—432no—
237#396—861no—
238#394—861no—
239#388—861no—
240#386—861no—
241#381—431no—
242#380—431no—
243#379—431no—
244C4×C22⋊C4—861no—
245#352—864no—
246AΣL(1,𝔽16)—864no—
247#343—21no—
248#342—861no—
249C43#1322211yescharacteristic, complemented, Sylow
250C25—431no—
251C22×D4—861no—
252C22×D4C22×D4311yescharacteristic
253C23×C4—431no—
254C23×C4C4×D4311yescharacteristic
255C23×C4D17211yescharacteristic
256C2×M16—22no—
257#123—862no—
258#123—862no—
259#120—862no—
260#120—862no—
261C4×D4—41no—
262C4×D4—41no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4C22⋊D4311yescharacteristic
266C2×C22⋊C4—431no—
267C2×C22⋊C4—431no—
268C2×C22⋊C4—862no—
269C2×C22⋊C4—861no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—861no—
272C2×C22⋊C4—861no—
273C2×C22⋊C4—861no—
274C2×C22⋊C4—861no—
275C2×C22⋊C4—1721no—
276C2×C22⋊C4—1721no—
277C2×C22⋊C4C4×D4311yescharacteristic
278C2×C22⋊C4D17211yescharacteristic
279C2×C42—1721no—
280C2×C42C22⋊D4311yescharacteristic
281C4⋊C8—41no—
282C4⋊C8—41no—
283#100—22no—
284#100—22no—
285#99—434no—
286#99—862no—
287#95—861no—
288#95—861no—
289#95—861no—
290#95—1721no—
291C24—861no—
292C24—862no—
293C24—3441no—
294C24—1721no—
295C24—1721no—
296C24—1722no—
297C24C2×C4×D4311yescharacteristic
298C24C2×D17211yescharacteristic
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—3441no—
302C2×D4—1722no—
303C2×D4—1722no—
304C2×D4D4×D4312yes—
305C2×D4#1062190212yes—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—81no—
311C22×C4—81no—
312C22×C4—862no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—1722no—
317C22×C4—1721no—
318C22×C4—1721no—
319C22×C4(C2×D43)⋊C411yescharacteristic
320C22×C4(C2×D43)⋊C411yescharacteristic
321C22×C4(C2×D43)⋊C411yescharacteristic
322C22×C4(C2×D43)⋊C411yescharacteristic
323C22×C4C2×C22⋊D4311yescharacteristic
324M16—42no—
325M16—42no—
326C2×C8—42no—
327C4⋊C4—41no—
328C4⋊C4—3441no—
329C4⋊C4—1721no—
330C4⋊C4—1721no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—862no—
334C22⋊C4—862no—
335C22⋊C4—864no—
336C22⋊C4—3441no—
337C22⋊C4—1722no—
338C22⋊C4—1722no—
339C22⋊C4—1722no—
340C22⋊C4—1722no—
341C22⋊C4—1721no—
342C22⋊C4—1721no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C42—21no—
346C42—21no—
347C42—3442no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—862no—
357C23—3442no—
358C23—3442no—
359C23—3444no—
360C23—3444no—
361C23—1721no—
362C23—1721no—
363C23—1721no—
364C23—1722no—
365C23—1722no—
366C23—1721no—
367C23—1721no—
368C23—1721no—
369C23C2×(C2×D43)⋊C411yescharacteristic
370C23#1306328712yes—
371C23#1306330012yes—
372D4—42no—
373D4—42no—
374D4—3444no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—3442no—
389C2×C4—3442no—
390C2×C4—3442no—
391C2×C4—1724no—
392C2×C4—1721no—
393C2×C4—1721no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4#1306323911yescharacteristic
402C2×C4#1306323911yescharacteristic
403C2×C4#1306331411yescharacteristic
404C2×C4#1306332111yescharacteristic
405C8—82no—
406C22—21no—
407C22—21no—
408C22—22no—
409C22—22no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—81no—
418C22—3441no—
419C22—3441no—
420C22—3444no—
421C22—3444no—
422C22—3441no—
423C22—3441no—
424C22—1722no—
425C22—1722no—
426C22—1722no—
427C22#1458280011yescharacteristic
428C22C2×#1306323911yescharacteristic
429C22#1458287211yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—3441no—
438C4—3441no—
439C4—3444no—
440C4—3441no—
441C2—21no—
442C2—21no—
443C2—42no—
444C2—42no—
445C2—3442no—
446C2#1913543011yescharacteristic
447C2#1913623711yescharacteristic
448C2#1913624211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC24×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1800C2
socleC22×C43C2×#99
prime radicalC2×#13063293C22
cosocleC22×D4×C43C23
hypercenter#1800D43
hypocenterC43#13222
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
2. C2×#14582690C2semidirect
4. C4×#13063240C2semidirect
5. C43×#1800C2semidirect
8. C22×(C2×D43)⋊C4C4semidirect
14. #14582760C4semidirect
15. #14582759C4semidirect
16. #14582754C4semidirect
220. #1800D43semidirect
249. C43#13222semidirect

Maximal subgroups

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

subgroupindex
#191394812
C2×#145826902
C2×#145826872
C4×#130632402
C43×#18002
#1322243