Finite Group Databasebeta

← #24996979

Subgroups — #24996979

Order 11008.

600 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 85 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#19140076C211yesmaximal, characteristic
2#19138878C211yesmaximal, characteristic, complemented
3#19134694C211yesmaximal, characteristic, complemented
4#19133124C211yesmaximal, characteristic
5#19132924C211yesmaximal, characteristic, complemented
6#19132449C211yesmaximal, characteristic, complemented
7C43×#3094C211yesmaximal, characteristic
8C22×Dic43⋊C4C2211yescharacteristic
9#14582863C2211yescharacteristic
10#14582837—21no—
11#14582837—21no—
12#14582830—21no—
13#14582813—21no—
14#14582793—22no—
15#14582783—22no—
16#14582779—21no—
17#14582779—21no—
18#14582771—21no—
19#14582762C2211yescharacteristic
20#14582760—21no—
21C4×C22⋊Dic43C2211yescharacteristic
22#14582658—22no—
23#14582633—22no—
24#14582624—22no—
25C2×#121×C43C2211yescharacteristic
26C2×#117×C43C2211yescharacteristic
27C43×#482—22no—
28C43×#481—21no—
29C43×#480—21no—
30C43×#428—21no—
31C43×#418—21no—
32C43×#407C2211yescharacteristic
33C23×Dic43D411yescharacteristic
34C23×Dic43D411yescharacteristic
35C2×#10621877—21no—
36C2×Dic43⋊C4—22no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×C22⋊Dic43—22no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—22no—
47C2×C4×Dic43D412yes—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C43⋊#95—22no—
51C43⋊#95—22no—
52C43⋊#95—22no—
53C43⋊#95—22no—
54C43⋊#95—22no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95D412yes—
58C22×D4×C43—21no—
59C22×D4×C43D411yescharacteristic
60C23×C4×C43C2311yescharacteristic
61C2×M16×C43—21no—
62#121×C43—21no—
63#121×C43—21no—
64#121×C43—21no—
65#121×C43—21no—
66#117×C43—21no—
67#117×C43—21no—
68#117×C43—21no—
69#117×C43—21no—
70C2×C4⋊C4×C43D411yescharacteristic
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C42×C43—21no—
76#107×C43—22no—
77#106×C43—22no—
78#102×C43—22no—
79#102×C43—22no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43D412yes—
82C24×C43—21no—
83C24×C43C2×D411yescharacteristic
84C2×D4×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—44no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—42no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—42no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C22×Dic43—21no—
101C22×Dic43—21no—
102C22×Dic43—22no—
103C22×Dic43—21no—
104C22×Dic43—22no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—42no—
109C22×Dic43—42no—
110M16×C43—42no—
111C2×C8×C43—22no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—21no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C42×C43—41no—
123C42×C43—41no—
124C22⋊Dic43—42no—
125C22⋊Dic43—42no—
126C22⋊Dic43—44no—
127C22⋊Dic43—82no—
128Dic43⋊C4—44no—
129Dic43⋊C4—41no—
130Dic43⋊C4—41no—
131Dic43⋊C4—41no—
132Dic43⋊C4—41no—
133C4×Dic43—42no—
134#10621877—42no—
135C2×C43⋊C8—41no—
136C23×C43—22no—
137C23×C43—22no—
138C23×C43—41no—
139C23×C43—42no—
140C23×C43—42no—
141C23×C43—41no—
142C23×C43—42no—
143C23×C43#12011yescharacteristic
144C23×C43#12011yescharacteristic
145C23×C43#12111yescharacteristic
146D4×C43—42no—
147D4×C43—81no—
148D4×C43—82no—
149D4×C43—82no—
150C2×C4×C43—22no—
151C2×C4×C43—22no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—42no—
162C2×C4×C43#12011yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×C4×C43#12711yescharacteristic
166C2×Dic43—22no—
167C2×Dic43—22no—
168C2×Dic43—22no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—42no—
177C2×Dic43—42no—
178C2×Dic43—41no—
179C2×Dic43—42no—
180C2×Dic43—42no—
181C2×Dic43—42no—
182C2×Dic43—81no—
183C8×C43—42no—
184C43⋊C8—81no—
185#9941—431nomaximal, Sylow
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—44no—
194C22×C43—84no—
195C22×C43—81no—
196C22×C43—81no—
197C22×C43—81no—
198C22×C43#39211yescharacteristic
199C22×C43#45412yes—
200C22×C43#45812yes—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—21no—
205C4×C43—81no—
206C4×C43—81no—
207C4×C43—81no—
208Dic43—42no—
209Dic43—82no—
210Dic43—82no—
211Dic43—81no—
212#3094D4311yescharacteristic
213#2591—431no—
214#2484—431no—
215#1826—431no—
216#1510—431no—
217#1463—431no—
218#1284—431no—
219C2×C43—22no—
220C2×C43—22no—
221C2×C43—41no—
222C2×C43—161no—
223C2×C43#200311yescharacteristic
224C2×C43#201011yescharacteristic
225C2×C43#202211yescharacteristic
226C2×#121C2×D4311yescharacteristic
227C2×#117C2×D4311yescharacteristic
228C22×C4⋊C4—431no—
229#482—22no—
230#481—21no—
231#480—21no—
232#428—21no—
233#418—21no—
234#407—431no—
235#407C2×D4311yescharacteristic
236#400—861no—
237#400—861no—
238#398—861no—
239#394—861no—
240#388—862no—
241#387—862no—
242#386—861no—
243#386—861no—
244#385—861no—
245#381—431no—
246#381—861no—
247C4×C22⋊C4—431no—
248#339—862no—
249#327—862no—
250#324—862no—
251C43#994111yescharacteristic, complemented, Sylow
252C22×D4—21no—
253C22×D4C22⋊D4311yescharacteristic
254C23×C4—431no—
255C23×C4—431no—
256C23×C4C22×D4311yescharacteristic
257C2×M16—21no—
258C2×M16—861no—
259#121—21no—
260#121—21no—
261#121—21no—
262#121—21no—
263#117—21no—
264#117—21no—
265#117—21no—
266#117—21no—
267C2×C4⋊C4—862no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4—861no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4—861no—
272C2×C4⋊C4—861no—
273C2×C4⋊C4—861no—
274C2×C4⋊C4C22⋊D4311yescharacteristic
275C2×C4⋊C4C22⋊D4311yescharacteristic
276C2×C4⋊C4C22⋊D4311yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—862no—
280C2×C22⋊C4—862no—
281C2×C22⋊C4—861no—
282C2×C22⋊C4—861no—
283C2×C42—21no—
284C2×C42—432no—
285#107—22no—
286#106—22no—
287#102—22no—
288#102—22no—
289C22⋊C8—21no—
290C22⋊C8—861no—
291C22⋊C8—861no—
292C22⋊C8C22⋊D4312yes—
293#95—432no—
294#95—862no—
295#95—862no—
296#95—862no—
297#95—862no—
298#95—862no—
299#95—861no—
300#95—861no—
301C24—21no—
302C24D4×D4311yescharacteristic
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—42no—
306C2×D4—44no—
307C2×D4—41no—
308C2×D4—41no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—42no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—862no—
318C22×C4—861no—
319C22×C4—862no—
320C22×C4—861no—
321C22×C4—1722no—
322C22×C4—1722no—
323C22×C4D4×D4311yescharacteristic
324C22×C4D4×D4311yescharacteristic
325C22×C4#1062190011yescharacteristic
326C22×C4C2×C22⋊D4311yescharacteristic
327C22×C4C2×C22⋊D4311yescharacteristic
328C22×C4C2×C22⋊D4311yescharacteristic
329M16—42no—
330M16—1722no—
331C2×C8—22no—
332C2×C8—1721no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—1724no—
340C4⋊C4—1721no—
341C4⋊C4—1721no—
342C4⋊C4—1721no—
343C4⋊C4—1721no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—3442no—
349C22⋊C4—1724no—
350C22⋊C4—1722no—
351C22⋊C4—1722no—
352C42—41no—
353C42—41no—
354C42—1722no—
355C23—22no—
356C23—22no—
357C23—41no—
358C23—42no—
359C23—42no—
360C23—41no—
361C23—42no—
362C23#1306329311yescharacteristic
363C23#1306329311yescharacteristic
364C23#1306329611yescharacteristic
365D4—42no—
366D4—81no—
367D4—82no—
368D4—82no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—862no—
382C2×C4—862no—
383C2×C4—862no—
384C2×C4—3441no—
385C2×C4—1722no—
386C2×C4—1722no—
387C2×C4—1722no—
388C2×C4—1722no—
389C2×C4—1722no—
390C2×C4—1721no—
391C2×C4—1722no—
392C2×C4—1722no—
393C2×C4—1722no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4#1306329411yescharacteristic
399C2×C4#1306329711yescharacteristic
400C2×C4#1306329711yescharacteristic
401C2×C4#1306332111yescharacteristic
402C8—42no—
403C8—3441no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—44no—
412C22—84no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22#1458280711yescharacteristic
417C22#1458307012yes—
418C22#1458308812yes—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—81no—
424C4—81no—
425C4—81no—
426C4—3442no—
427C4—3442no—
428C4—3441no—
429C4—1722no—
430C2—22no—
431C2—22no—
432C2—41no—
433C2—161no—
434C2#1913561411yescharacteristic
435C2#1913565911yescharacteristic
436C2#1913572311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#3094C2
socleC22×C43#392
prime radicalC2×#121×C43C22
hypercenter#3094D43
hypocenterC43#9941
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
2. #19138878C2semidirect
3. #19134694C2semidirect
5. #19132924C2semidirect
6. #19132449C2semidirect
251. C43#9941semidirect

Maximal subgroups

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

subgroupindex
#191400762
#191388782
#191346942
#191331242
#191329242
#191324492
C43×#30942
#994143