Finite Group Databasebeta

← #25014913

Subgroups — #25014913

Order 11008.

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

normal subgroups only

This group has 602 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#19139562C211yesmaximal, characteristic
2C2×#14582693C212yesmaximal, complemented
3C2×#14582691C212yesmaximal
4C4×#13063240C211yesmaximal, characteristic, complemented
5C43×#1799C211yesmaximal, characteristic, complemented
6C2×#13063321C2211yescharacteristic
7C2×#13063313C411yescharacteristic, complemented
8C2×#13063312C2211yescharacteristic
9C2×#13063240C2212yes—
10#14582815—21no—
11#14582815—21no—
12#14582804C411yescharacteristic, complemented
13#14582800C411yescharacteristic, complemented
14#14582778—21no—
15#14582778—21no—
16C4×C4⋊Dic43C411yescharacteristic, complemented
17C4×C22⋊Dic43—21no—
18#14582693—24no—
19#14582691—24no—
20#14582666—21no—
21C2×C4×D4×C43C2211yescharacteristic
22C2×#99×C43C2212yes—
23C43×#380—21no—
24C43×#342—21no—
25C22×Dic86C2×C411yescharacteristic
26C22×D172C2×C411yescharacteristic
27C22×C22⋊D43—21no—
28C22×C22⋊D43—21no—
29#13063321—22no—
30#13063321—22no—
31#13063313—41no—
32#13063313—41no—
33#13063312—22no—
34#13063312—22no—
35C2×C4⋊Dic43—21no—
36C2×C22⋊Dic43—22no—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×C4×Dic43—41no—
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43C2×C411yescharacteristic
46#13063240—22no—
47#13063240D414yes—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—41no—
52C22×D4×C43C2311yescharacteristic
53C23×C4×C43D411yescharacteristic
54C23×C4×C43D411yescharacteristic
55C4×D4×C43—41no—
56C4×D4×C43—41no—
57C2×C4⋊C4×C43—41no—
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C22⋊C4×C43—22no—
60C2×C22⋊C4×C43D411yescharacteristic
61C2×C22⋊C4×C43D411yescharacteristic
62C2×C42×C43C2×C411yescharacteristic
63#99×C43—22no—
64#99×C43—22no—
65#95×C43—41no—
66C24×C43C2×D411yescharacteristic
67C24×C43C2×D411yescharacteristic
68C23×D43—21no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43C2×D412yes—
72C2×D4×C43#4112yes—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—42no—
78C22×C4×C43—81no—
79C22×C4×C43—81no—
80C22×C4×C43C22⋊C411yescharacteristic
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22⋊C411yescharacteristic
83C22×C4×C43C22⋊C411yescharacteristic
84C22×C4×C43C22×C411yescharacteristic
85C2×C22⋊D43—42no—
86C2×C22⋊D43—42no—
87C2×C22⋊D43—42no—
88C2×C22⋊D43—41no—
89C2×C22⋊D43—41no—
90C2×C22⋊D43—81no—
91C2×C22⋊D43—81no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—42no—
96C2×D172—22no—
97C2×D172—41no—
98C2×D172—41no—
99C2×Dic86—22no—
100C2×Dic86—41no—
101C2×Dic86—41no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—82no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—42no—
107C22⋊C4×C43—42no—
108C42×C43—21no—
109C42×C43—21no—
110C22⋊Dic43—24no—
111C22⋊Dic43—42no—
112C22⋊Dic43—42no—
113C22⋊Dic43—41no—
114C22⋊Dic43—41no—
115(C2×D43)⋊C4—42no—
116(C2×D43)⋊C4—41no—
117(C2×D43)⋊C4—41no—
118(C2×D43)⋊C4—81no—
119(C2×D43)⋊C4—81no—
120C4⋊Dic43—42no—
121C4×Dic43—22no—
122C4×Dic43—22no—
123C4×Dic43—82no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—21no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43C2×C22⋊C411yescharacteristic
133C23×C43#12112yes—
134C23×C43#12411yescharacteristic
135C23×C43#12711yescharacteristic
136C22×D43—41no—
137C22×D43—41no—
138C22×D43—41no—
139C22×D43—41no—
140C22×D43—41no—
141C22×D43—41no—
142C22×D43—41no—
143D4×C43—42no—
144D4×C43—42no—
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—42no—
152C2×C4×C43—42no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—81no—
157C2×C4×C43—81no—
158C2×C4×C43—82no—
159C2×C4×C43—82no—
160C2×C4×C43—82no—
161C2×C4×C43#9911yescharacteristic
162C2×C4×C43#9911yescharacteristic
163C2×C4×C43C4×D412yes—
164C22⋊D43—84no—
165C22⋊D43—82no—
166C22⋊D43—82no—
167C2×Dic43—22no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—44no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—82no—
178C2×Dic43—82no—
179D172—82no—
180Dic86—82no—
181#13225—431nomaximal, Sylow
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—22no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—42no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—41no—
194C22×C43—81no—
195C22×C43—81no—
196C22×C43#39011yescharacteristic
197C22×C43C2×#9911yescharacteristic
198C22×C43#41011yescharacteristic
199C2×D43—81no—
200C2×D43—81no—
201C2×D43—81no—
202C2×D43—81no—
203C2×D43—81no—
204C2×D43—81no—
205C2×D43—81no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—22no—
209C4×C43—41no—
210C4×C43—41no—
211C4×C43—41no—
212C4×C43—162no—
213Dic43—42no—
214Dic43—81no—
215Dic43—84no—
216Dic43—81no—
217#2544—431no—
218C2×#354—432no—
219C2×#353—432no—
220#1799D4311yescharacteristic, complemented
221C4×#99—431no—
222C2×C43—21no—
223C2×C43—21no—
224C2×C43—42no—
225C2×C43—41no—
226C2×C43—41no—
227C2×C43#196411yescharacteristic
228C2×C43#212611yescharacteristic
229C2×C43#212711yescharacteristic
230D43—161no—
231C2×#127—431no—
232C2×#124—431no—
233C2×#124—431no—
234C2×C4×D4C2×D4311yescharacteristic
235C2×#99—432no—
236C2×#99C2×D4312yes—
237#394—861no—
238#394—861no—
239#391—431no—
240#390—431no—
241#386—861no—
242#386—861no—
243#380—21no—
244C4×C4⋊C4—431no—
245C4×C22⋊C4—861no—
246#354—864no—
247#353—864no—
248#342—21no—
249#342—861no—
250C43#1322511yescharacteristic, complemented, Sylow
251C22×Q8—431no—
252C22×D4—431no—
253C22×D4—861no—
254C22×D4—861no—
255C22×D4C22×D4311yescharacteristic
256C23×C4D17211yescharacteristic
257C23×C4C22⋊D4311yescharacteristic
258#127—862no—
259#127—862no—
260#124—862no—
261#124—862no—
262#124—1721no—
263#124—1721no—
264C4×D4—41no—
265C4×D4—41no—
266C2×C4⋊C4—41no—
267C2×C4⋊C4—861no—
268C2×C4⋊C4C4×D4311yescharacteristic
269C2×C22⋊C4—22no—
270C2×C22⋊C4—862no—
271C2×C22⋊C4—861no—
272C2×C22⋊C4—861no—
273C2×C22⋊C4—861no—
274C2×C22⋊C4—861no—
275C2×C22⋊C4—861no—
276C2×C22⋊C4—861no—
277C2×C22⋊C4D17211yescharacteristic
278C2×C22⋊C4C22⋊D4311yescharacteristic
279C2×C42—431no—
280C2×C42—431no—
281C2×C42—1721no—
282C2×C42C4×D4311yescharacteristic
283#99—22no—
284#99—22no—
285#99—434no—
286#99—862no—
287#95—41no—
288#95—861no—
289#95—861no—
290#95—861no—
291#95—1721no—
292C24—861no—
293C24C2×D17211yescharacteristic
294C24C2×C22⋊D4311yescharacteristic
295C2×Q8—862no—
296C2×Q8—1721no—
297C2×Q8—1721no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—862no—
301C2×D4—3441no—
302C2×D4—3441no—
303C2×D4—1721no—
304C2×D4—1721no—
305C2×D4—1722no—
306C2×D4—1722no—
307C2×D4—1722no—
308C2×D4—1721no—
309C2×D4—1721no—
310C2×D4D4×D4312yes—
311C2×D4#1062190212yes—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—42no—
317C22×C4—81no—
318C22×C4—81no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—1722no—
323C22×C4(C2×D43)⋊C411yescharacteristic
324C22×C4(C2×D43)⋊C411yescharacteristic
325C22×C4(C2×D43)⋊C411yescharacteristic
326C22×C4(C2×D43)⋊C411yescharacteristic
327C22×C4C2×C4×D4311yescharacteristic
328C4⋊C4—41no—
329C4⋊C4—82no—
330C4⋊C4—1722no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—864no—
336C22⋊C4—3441no—
337C22⋊C4—3441no—
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—862no—
348C42—862no—
349C42—3442no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—1721no—
359C23—1721no—
360C23—1721no—
361C23—1721no—
362C23—1721no—
363C23—1721no—
364C23—1721no—
365C23C2×(C2×D43)⋊C411yescharacteristic
366C23#1306330012yes—
367C23#1306331411yescharacteristic
368C23#1306332111yescharacteristic
369Q8—3442no—
370D4—42no—
371D4—42no—
372D4—3442no—
373D4—3444no—
374D4—3442no—
375D4—3442no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—862no—
393C2×C4—3442no—
394C2×C4—3442no—
395C2×C4—1724no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4#1306323911yescharacteristic
405C2×C4#1306323911yescharacteristic
406C2×C4#1306328712yes—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—22no—
411C22—21no—
412C22—42no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—81no—
420C22—81no—
421C22—3441no—
422C22—3441no—
423C22—3441no—
424C22—3441no—
425C22—3441no—
426C22—3441no—
427C22—3441no—
428C22#1458280011yescharacteristic
429C22C2×#1306323911yescharacteristic
430C22#1458287211yescharacteristic
431C4—21no—
432C4—21no—
433C4—22no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—162no—
438C4—3441no—
439C4—3444no—
440C4—3441no—
441C4—1722no—
442C2—21no—
443C2—21no—
444C2—41no—
445C2—42no—
446C2—41no—
447C2—6881no—
448C2#1913543011yescharacteristic
449C2#1913625811yescharacteristic
450C2#1913626211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1799C2
socleC22×C43C2×#99
prime radicalC2×#13063321C22
cosocleC22×D4×C43C23
hypercenter#1799D43
hypocenterC43#13225
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. C2×#14582693C2semidirect
4. C4×#13063240C2semidirect
5. C43×#1799C2semidirect
7. C2×#13063313C4semidirect
12. #14582804C4semidirect
13. #14582800C4semidirect
16. C4×C4⋊Dic43C4semidirect
220. #1799D43semidirect
250. C43#13225semidirect

Maximal subgroups

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

subgroupindex
#191395622
C2×#145826932
C2×#145826912
C4×#130632402
C43×#17992
#1322543