Finite Group Databasebeta

← #25015252

Subgroups — #25015252

Order 11008.

488 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 93 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#19138909C211yesmaximal, characteristic
2#19134585C211yesmaximal, characteristic
3#99×Dic43C211yesmaximal, characteristic
4#19132714C211yesmaximal, characteristic
5#19132713C211yesmaximal, characteristic
6#19132712C211yesmaximal, characteristic
7C43×#1390C211yesmaximal, characteristic
8C2×D4×Dic43C2211yescharacteristic
9C22×Dic43⋊C4C411yescharacteristic, complemented
10#14582922—21no—
11C2×#13063242C2211yescharacteristic
12C2×#13063240C2211yescharacteristic
13#14582841—21no—
14#14582835—21no—
15#14582796—21no—
16#14582779C2211yescharacteristic
17#14582774C411yescharacteristic, complemented
18#14582772C411yescharacteristic, complemented
19#14582757—21no—
20#14582757C411yescharacteristic, complemented
21C22⋊C4×Dic43—21no—
22#14582667—21no—
23#14582665—21no—
24C2×#100×C43C2211yescharacteristic
25C2×#99×C43C2211yescharacteristic
26C43×#386C2211yescharacteristic
27C23×Dic43C2×C411yescharacteristic
28C23×Dic43C2×C411yescharacteristic
29C23×Dic43D411yescharacteristic
30C2×#10621877—21no—
31D4×Dic43—41no—
32D4×Dic43—41no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43D411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—41no—
40C2×Dic43⋊C4—41no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43C2×C411yescharacteristic
44C2×C22⋊Dic43C2×C411yescharacteristic
45C2×C22⋊Dic43D411yescharacteristic
46C2×C4×Dic43—41no—
47C2×C4×Dic43D411yescharacteristic
48Dic43⋊C8—41no—
49Dic43⋊C8—41no—
50#13063242—21no—
51#13063242—21no—
52#13063240—21no—
53#13063240Q812yes—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—41no—
59C22×D4×C43C2311yescharacteristic
60C23×C4×C43C2×C411yescharacteristic
61C2×M16×C43—21no—
62C2×C22⋊C4×C43—21no—
63C2×C22⋊C4×C43—21no—
64C2×C22⋊C4×C43C2×C411yescharacteristic
65#100×C43—21no—
66#100×C43—21no—
67#99×C43—21no—
68#99×C43Q812yes—
69#95×C43—21no—
70C24×C43C22×C411yescharacteristic
71C24×C43C2×D411yescharacteristic
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43C2×Q811yescharacteristic
75C2×D4×C43C2×Q811yescharacteristic
76C2×D4×C43#4111yescharacteristic
77C2×D4×C43#4111yescharacteristic
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43—81no—
83C22×C4×C43C2×D411yescharacteristic
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—41no—
91C22×Dic43—41no—
92C22×Dic43—42no—
93C22×Dic43—42no—
94C22×Dic43—81no—
95C22×Dic43C22⋊C411yescharacteristic
96C22×Dic43C22⋊C411yescharacteristic
97C22×Dic43C22⋊C411yescharacteristic
98C22×Dic43C22⋊C411yescharacteristic
99M16×C43—41no—
100M16×C43—41no—
101C2×C8×C43—41no—
102C22⋊C4×C43—22no—
103C22⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—81no—
106C22⋊Dic43—22no—
107C22⋊Dic43—41no—
108C22⋊Dic43—41no—
109C22⋊Dic43—41no—
110C22⋊Dic43—41no—
111C22⋊Dic43—81no—
112C4⋊Dic43—41no—
113C4⋊Dic43—81no—
114Dic43⋊C4—42no—
115Dic43⋊C4—42no—
116Dic43⋊C4—41no—
117Dic43⋊C4—41no—
118Dic43⋊C4—81no—
119C4×Dic43—21no—
120C4×Dic43—21no—
121C4×Dic43—82no—
122#10621877—41no—
123#10621877—41no—
124C2×C43⋊C8—41no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—21no—
128C23×C43—21no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43—41no—
133C23×C43C2×C22⋊C411yescharacteristic
134C23×C43C4×Q811yescharacteristic
135C23×C43C4×Q811yescharacteristic
136C23×C43C22⋊Q811yescharacteristic
137C23×C43C22⋊Q811yescharacteristic
138D4×C43—41no—
139D4×C43—41no—
140D4×C43—41no—
141D4×C43—41no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43—82no—
154C2×C4×C43#12411yescharacteristic
155C2×C4×C43C4⋊Q811yescharacteristic
156C2×Dic43—22no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159C2×Dic43—21no—
160C2×Dic43—42no—
161C2×Dic43—42no—
162C2×Dic43—42no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—42no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—81no—
174C2×Dic43—81no—
175C2×Dic43—81no—
176C2×Dic43—82no—
177C2×Dic43#9911yescharacteristic
178C2×Dic43#9911yescharacteristic
179C8×C43—81no—
180C43⋊C8—81no—
181#13295—431nomaximal, Sylow
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—42no—
193C22×C43—41no—
194C22×C43—41no—
195C22×C43—41no—
196C22×C43—41no—
197C22×C43—81no—
198C22×C43#39111yescharacteristic
199C22×C43C2×#9911yescharacteristic
200C22×C43#41011yescharacteristic
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—81no—
204C4×C43—82no—
205C4×C43—81no—
206Dic43—21no—
207Dic43—41no—
208Dic43—41no—
209Dic43—41no—
210Dic43—81no—
211Dic43—82no—
212Dic43—81no—
213Dic43#35212yes—
214#2487—431no—
215#1800—431no—
216C4×#99—431no—
217#1390—431no—
218#1390—431no—
219#1390—431no—
220#1390D4311yescharacteristic
221C2×C43—21no—
222C2×C43—21no—
223C2×C43—41no—
224C2×C43—41no—
225C2×C43—41no—
226C2×C43—41no—
227C2×C43#199611yescharacteristic
228C2×C43C2×#35211yescharacteristic
229C2×C43#212211yescharacteristic
230C2×C4×D4—431no—
231C22×C4⋊C4—431no—
232#423—861no—
233C2×#100—431no—
234C2×#100C2×D4311yescharacteristic
235C2×#99—431no—
236C2×#99C2×D4311yescharacteristic
237#400—861no—
238#399—861no—
239#389—861no—
240#386—431no—
241#386C2×D4311yescharacteristic
242#385—431no—
243#385—431no—
244#380—431no—
245#380—861no—
246C4×C22⋊C4—861no—
247#343—861no—
248#342—861no—
249C43#1329511yescharacteristic, complemented, Sylow
250C22×D4C22×D4311yescharacteristic
251C23×C4—431no—
252C23×C4—431no—
253C23×C4—431no—
254C23×C4C4×D4311yescharacteristic
255C2×M16—21no—
256C2×M16—861no—
257C4×D4—1721no—
258C4×D4—1721no—
259C2×C4⋊C4—431no—
260C2×C4⋊C4—861no—
261C2×C4⋊C4—861no—
262C2×C4⋊C4—861no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4—1721no—
266C2×C4⋊C4—1721no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—431no—
270C2×C22⋊C4—431no—
271C2×C22⋊C4—431no—
272C2×C22⋊C4—861no—
273C2×C22⋊C4—861no—
274C2×C22⋊C4C4×D4311yescharacteristic
275C2×C42—431no—
276C2×C42—1721no—
277C4⋊C8—1721no—
278C4⋊C8—1721no—
279#100—21no—
280#100—21no—
281#100—861no—
282#100—861no—
283#99—21no—
284#99—432no—
285#99—861no—
286#99Dic8612yes—
287#95—21no—
288#95—861no—
289#95—861no—
290#95—861no—
291#95—861no—
292#95—1721no—
293C24C2×C4×D4311yescharacteristic
294C24D4×D4311yescharacteristic
295C2×D4—41no—
296C2×D4—41no—
297C2×D4C2×Dic8611yescharacteristic
298C2×D4#1062189811yescharacteristic
299C2×D4#1062190011yescharacteristic
300C2×D4Q8×D4311yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—81no—
306C22×C4—431no—
307C22×C4—431no—
308C22×C4—431no—
309C22×C4—431no—
310C22×C4—861no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—3441no—
317C22×C4—1722no—
318C22×C4—1722no—
319C22×C4—1721no—
320C22×C4—1721no—
321C22×C4D4×D4311yescharacteristic
322M16—41no—
323M16—41no—
324M16—1721no—
325M16—1721no—
326C2×C8—41no—
327C2×C8—1721no—
328C4⋊C4—3441no—
329C4⋊C4—3441no—
330C4⋊C4—1721no—
331C4⋊C4—1721no—
332C4⋊C4—1721no—
333C4⋊C4—1722no—
334C4⋊C4—1722no—
335C22⋊C4—22no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—81no—
339C22⋊C4—862no—
340C22⋊C4—3441no—
341C22⋊C4—1721no—
342C22⋊C4—1721no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C42—861no—
346C42—861no—
347C42—3442no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23C22⋊C4×D4311yescharacteristic
357C23#1306329011yescharacteristic
358C23C4×Dic8611yescharacteristic
359C23#1306330211yescharacteristic
360C23#1306330311yescharacteristic
361D4—41no—
362D4—41no—
363D4—41no—
364D4—41no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4—431no—
378C2×C4—431no—
379C2×C4—862no—
380C2×C4—861no—
381C2×C4—861no—
382C2×C4—861no—
383C2×C4—3441no—
384C2×C4—3441no—
385C2×C4—3441no—
386C2×C4—3442no—
387C2×C4—1722no—
388C2×C4—1722no—
389C2×C4—1722no—
390C2×C4—1722no—
391C2×C4—1721no—
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#1306331111yescharacteristic
401C2×C4#1306332411yescharacteristic
402C8—81no—
403C8—3441no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—81no—
420C22#1458280311yescharacteristic
421C22#99×D4311yescharacteristic
422C22#1458287111yescharacteristic
423C4—21no—
424C4—21no—
425C4—81no—
426C4—82no—
427C4—81no—
428C4—432no—
429C4—861no—
430C4—3441no—
431C4—3442no—
432C4—3441no—
433C4—1721no—
434C4—1721no—
435C4—1721no—
436C2—21no—
437C2—21no—
438C2—41no—
439C2—41no—
440C2—41no—
441C2—41no—
442C2#1913557811yescharacteristic
443C2#352×D4311yescharacteristic
444C2#1913624311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC24×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1390C2
socleC22×C43C2×#99
prime radical, cosocleC22×D4×C43C23
hypercenter#1390D43
hypocenterC43#13295
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1390

Complements

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

NH ≅ G/Ntype
9. C22×Dic43⋊C4C4semidirect
17. #14582774C4semidirect
18. #14582772C4semidirect
20. #14582757C4semidirect
249. C43#13295semidirect

Maximal subgroups

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

subgroupindex
#191389092
#191345852
#99×Dic432
#191327142
#191327132
#191327122
C43×#13902
#1329543