Finite Group Databasebeta

← #24994627

Subgroups — #24994627

Order 11008.

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

normal subgroups only

This group has 472 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#19144518C211yesmaximal, characteristic
2#19143640C211yesmaximal, characteristic
3#19134675C211yesmaximal, characteristic, complemented
4#19133136C211yesmaximal, characteristic
5#19132501C211yesmaximal, characteristic, complemented
6#19132472C211yesmaximal, characteristic, complemented
7C43×#1824C211yesmaximal, characteristic, complemented
8#14583410C2211yescharacteristic
9#14583234—21no—
10#14583229C412yescomplemented
11#14583217—21no—
12#14583212C412yescomplemented
13#14582974—21no—
14#14582973—21no—
15#14582970—21no—
16C8×C22⋊D43—21no—
17#14582957—21no—
18#14582939—21no—
19#14582898—21no—
20#14582864—21no—
21#14582863C2211yescharacteristic
22#14582863C2211yescharacteristic
23#14582863C2211yescharacteristic
24#14582668—21no—
25#14582668—21no—
26#14582635—21no—
27#14582632—21no—
28C22×C4⋊C4×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C43×#380C2211yescharacteristic
31C43×#340—21no—
32C43×#340—21no—
33C2×#10621898D411yescharacteristic
34C2×#10621877—21no—
35C2×#10621877—21no—
36C2×#10621877D411yescharacteristic
37C2×#10621877D411yescharacteristic
38C2×#10621872—21no—
39C2×C8×D43—21no—
40#13063308—21no—
41#13063304C2×C411yescharacteristic
42#13063304D411yescharacteristic
43#13063299C2×C411yescharacteristic
44#13063299D411yescharacteristic
45#13063294—21no—
46C4×C22⋊D43—21no—
47C4×C22⋊D43—21no—
48#13063284D411yescharacteristic
49#13063258—22no—
50#13063256—22no—
51Dic43⋊C8—21no—
52Dic43⋊C8—21no—
53#13063248—22no—
54#13063245—22no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)C2×C412yes—
61(C2×D43)⋊C8—21no—
62(C2×D43)⋊C8—21no—
63#13063235—21no—
64C8×Dic43—21no—
65C23×C4×C43—21no—
66C23×C4×C43C2311yescharacteristic
67C22×C8×C43D411yescharacteristic
68C22×C8×C43D411yescharacteristic
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43C2×C412yes—
76C2×C22⋊C4×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79#95×C43—21no—
80C24×C43#4111yescharacteristic
81C22×C4×C43—22no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—82no—
88C22×C4×C43C22×C411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C2×C22⋊D43—21no—
95C2×C22⋊D43—21no—
96C2×C22⋊D43—21no—
97#10621898—41no—
98#10621898—41no—
99C2×D172C22⋊C411yescharacteristic
100C2×C4×D43—21no—
101C2×Dic86C22⋊C411yescharacteristic
102C2×C8×C43—21no—
103C2×C8×C43—21no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C22⋊C4×C43—81no—
113C22⋊Dic43—21no—
114C22⋊Dic43—21no—
115C22⋊Dic43—21no—
116(C2×D43)⋊C4—21no—
117(C2×D43)⋊C4—21no—
118C4⋊Dic43C22⋊C411yescharacteristic
119C4⋊Dic43C22⋊C411yescharacteristic
120Dic43⋊C4—21no—
121Dic43⋊C4—21no—
122C4×Dic43—21no—
123#10621877—41no—
124#10621877—41no—
125#10621877—41no—
126#10621877—41no—
127#10621877—41no—
128#10621877—41no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—21no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—41no—
133#10621872—81no—
134C8×D43—81no—
135C23×C43—21no—
136C23×C43—21no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43C4×D411yescharacteristic
140C23×C43#12111yescharacteristic
141C23×C43#12311yescharacteristic
142C22×D43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—82no—
154C2×C4×C43—82no—
155C2×C4×C43—82no—
156C2×C4×C43—81no—
157C2×C4×C43—81no—
158C2×C4×C43—81no—
159C2×C4×C43C2×C22⋊C411yescharacteristic
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43#12011yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C22⋊D43—41no—
164C22⋊D43—41no—
165C22⋊D43—81no—
166C22⋊D43—81no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170D172—41no—
171C4×D43—41no—
172C4×D43—41no—
173Dic86—41no—
174C8×C43—41no—
175C8×C43—41no—
176C43⋊C8—42no—
177C43⋊C8—41no—
178C43⋊C8—41no—
179C43⋊C8—81no—
180#9521—431nomaximal, Sylow
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—42no—
190C22×C43—42no—
191C22×C43#38611yescharacteristic
192C22×C43#47111yescharacteristic
193C22×C43#47311yescharacteristic
194C2×D43—41no—
195C2×D43—41no—
196C2×D43—41no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—82no—
201C4×C43—161no—
202C4×C43#45811yescharacteristic
203C4×C43#45811yescharacteristic
204Dic43—41no—
205Dic43—41no—
206Dic43—41no—
207#3092—431no—
208#2976—431no—
209#1824D4311yescharacteristic, complemented
210#1821—431no—
211#1513—431no—
212#1305—431no—
213#1293—431no—
214C2×C43—21no—
215C2×C43—21no—
216C2×C43—41no—
217C2×C43—41no—
218C2×C43#189011yescharacteristic
219C2×C43#190311yescharacteristic
220C2×C43#190811yescharacteristic
221D43—81no—
222#525—431no—
223C22×C4⋊C4C2×D4311yescharacteristic
224#484—861no—
225#483—432no—
226#481—861no—
227#480—432no—
228#436—861no—
229#435—861no—
230#435—861no—
231C8×D4—861no—
232#433—861no—
233#428—861no—
234#417—861no—
235#408—861no—
236#407—431no—
237#407—431no—
238#407—431no—
239C2×C22⋊C8C2×D4311yescharacteristic
240#380C2×D4311yescharacteristic
241#343—861no—
242#343—861no—
243#340—21no—
244#340—21no—
245#328—861no—
246#327—861no—
247C43#952111yescharacteristic, complemented, Sylow
248C2×#41—431no—
249C23×C4—21no—
250C23×C4C22×D4311yescharacteristic
251C2×M16—431no—
252C2×M16—431no—
253C2×M16—861no—
254C2×M16—861no—
255C2×M16—861no—
256C22×C8—861no—
257C22×C8C22⋊D4311yescharacteristic
258C22×C8C22⋊D4311yescharacteristic
259#123—861no—
260C22⋊Q8—431no—
261C22⋊Q8—431no—
262#121—431no—
263#121—431no—
264#120—861no—
265C4×D4—861no—
266C4×D4—861no—
267#117—431no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4C4×D4312yes—
275C2×C22⋊C4—21no—
276#107—862no—
277#106—862no—
278C4⋊C8—861no—
279C4⋊C8—861no—
280#103—862no—
281#102—862no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—432no—
285C22⋊C8—861no—
286C22⋊C8—861no—
287C22⋊C8—861no—
288C22⋊C8—861no—
289C22⋊C8—861no—
290C22⋊C8—861no—
291C22⋊C8—861no—
292#97—861no—
293C4×C8—861no—
294#95—21no—
295C24#1062190011yescharacteristic
296#41—1721no—
297#41—1721no—
298C2×Q8—431no—
299C2×D4—431no—
300C2×D4—861no—
301C2×D4—861no—
302C2×D4—861no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—82no—
310C22×C4—861no—
311C22×C4C2×C4×D4311yescharacteristic
312C22×C4#1062189811yescharacteristic
313C22×C4D4×D4311yescharacteristic
314C22×C4D4×D4311yescharacteristic
315C22×C4D4×D4311yescharacteristic
316C22×C4C2×C22⋊D4311yescharacteristic
317M16—3441no—
318M16—1721no—
319M16—1721no—
320M16—1721no—
321M16—1721no—
322M16—1721no—
323M16—1721no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—862no—
329C2×C8—861no—
330C2×C8—861no—
331C2×C8—3441no—
332C2×C8—1721no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—431no—
340C4⋊C4—431no—
341C4⋊C4—861no—
342C4⋊C4—861no—
343C22⋊C4—81no—
344C22⋊C4—861no—
345C22⋊C4—861no—
346C22⋊C4—861no—
347C22⋊C4—861no—
348C22⋊C4—861no—
349C42—861no—
350C23—21no—
351C23—21no—
352C23—41no—
353C23—41no—
354C23—861no—
355C23(C22⋊D43)⋊C411yescharacteristic
356C23#1306329611yescharacteristic
357C23#1306330711yescharacteristic
358Q8—1721no—
359D4—3441no—
360D4—3441no—
361D4—1721no—
362D4—1721no—
363D4—1721no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—861no—
381C2×C4—861no—
382C2×C4—861no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4C22⋊C4×D4311yescharacteristic
386C2×C4C4×C22⋊D4311yescharacteristic
387C2×C4#1306329311yescharacteristic
388C2×C4#1306329811yescharacteristic
389C8—41no—
390C8—41no—
391C8—3441no—
392C8—1722no—
393C8—1721no—
394C8—1721no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—42no—
404C22—42no—
405C22—1721no—
406C22—1721no—
407C22—1721no—
408C22#1458277511yescharacteristic
409C22#1458315911yescharacteristic
410C22#1458317111yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—82no—
415C4—161no—
416C4—1721no—
417C4—1721no—
418C4—1721no—
419C4#1458308811yescharacteristic
420C4#1458308811yescharacteristic
421C2—21no—
422C2—21no—
423C2—41no—
424C2—41no—
425C2—3441no—
426C2#1913500511yescharacteristic
427C2#1913507211yescharacteristic
428C2#1913511311yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1824C2
socleC22×C43#386
prime radical#14583410C22
cosocleC23×C4×C43C23
hypercenter#1824D43
hypocenterC43#9521
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
3. #19134675C2semidirect
5. #19132501C2semidirect
6. #19132472C2semidirect
7. C43×#1824C2semidirect
10. #14583229C4semidirect
12. #14583212C4semidirect
209. #1824D43semidirect
247. C43#9521semidirect

Maximal subgroups

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

subgroupindex
#191445182
#191436402
#191346752
#191331362
#191325012
#191324722
C43×#18242
#952143