Finite Group Databasebeta

← #24993779

Subgroups — #24993779

Order 11008.

732 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 111 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#19143855C211yesmaximal, characteristic
2#19135579C211yesmaximal, characteristic, complemented
3#19134539C211yesmaximal, characteristic
4#19133114C211yesmaximal, characteristic, complemented
5#19132501C211yesmaximal, characteristic, complemented
6#19132481C211yesmaximal, characteristic, complemented
7C43×#2341C211yesmaximal, characteristic
8C2×#13063355C412yescomplemented
9C2×#13063304C2211yescharacteristic
10#14583061—22no—
11#14583055—21no—
12#14583050—21no—
13C2×#13063252—22no—
14#14582900C412yescomplemented
15#14582863C2211yescharacteristic
16#14582863C2211yescharacteristic
17C4×C22⋊Dic43C2211yescharacteristic
18#14582665—22no—
19#14582635—21no—
20#14582635—21no—
21C22×#41×C43C2211yescharacteristic
22C2×C4×Q8×C43—21no—
23C43×#390—21no—
24C43×#390—22no—
25C43×#380—21no—
26C43×#380C2211yescharacteristic
27C4×C22⋊C4×C43—21no—
28C4×C22⋊C4×C43C2211yescharacteristic
29C22×Dic86C2×C411yescharacteristic
30#13063355—44no—
31C2×#10621885—22no—
32C2×#10621883—22no—
33C2×#10621877—21no—
34C2×#10621877C2×C412yes—
35#13063304—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C4×Dic43—21no—
44#13063252—44no—
45#13063249—22no—
46#13063246—22no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C43⋊#95—21no—
52C2×#41×C43—21no—
53C2×#41×C43—21no—
54C2×#41×C43—44no—
55C2×#41×C43C2×C412yes—
56C2×#41×C43D412yes—
57C22×Q8×C43D411yescharacteristic
58C22×D4×C43—21no—
59C22×D4×C43D411yescharacteristic
60C23×C4×C43—21no—
61C23×C4×C43C2311yescharacteristic
62C4×Q8×C43—44no—
63C2×C4⋊C4×C43—22no—
64C2×C4⋊C4×C43—21no—
65C2×C22⋊C4×C43—22no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—22no—
68C2×C22⋊C4×C43D412yes—
69C2×C42×C43—22no—
70C2×C42×C43—21no—
71#95×C43—21no—
72#95×C43D411yescharacteristic
73#95×C43D411yescharacteristic
74C24×C43—21no—
75C24×C43C2×D411yescharacteristic
76#41×C43—24no—
77#41×C43—24no—
78#41×C43—42no—
79#41×C43—42no—
80#41×C43—44no—
81#41×C43—44no—
82C2×Q8×C43—24no—
83C2×Q8×C43—21no—
84C2×Q8×C43C22⋊C412yes—
85C2×D4×C43—21no—
86C2×D4×C43—22no—
87C2×D4×C43—22no—
88C2×D4×C43—42no—
89C2×D4×C43—44no—
90C2×D4×C43C22⋊C412yes—
91C22×C4×C43—22no—
92C22×C4×C43—22no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—22no—
96C22×C4×C43—21no—
97C22×C4×C43—42no—
98C22×C4×C43—44no—
99C22×C4×C43C22×C411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—41no—
108C2×Dic86—21no—
109C2×Dic86—21no—
110C2×Dic86—42no—
111C4⋊C4×C43—44no—
112C4⋊C4×C43—42no—
113C22⋊C4×C43—42no—
114C22⋊C4×C43—42no—
115C22⋊C4×C43—44no—
116C22⋊C4×C43—82no—
117C42×C43—44no—
118C42×C43—42no—
119C22⋊Dic43—22no—
120C22⋊Dic43—41no—
121C22⋊Dic43—41no—
122C22⋊Dic43—41no—
123#10621885—44no—
124#10621883—44no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127Dic43⋊C4—41no—
128Dic43⋊C4—41no—
129C4×Dic43—42no—
130#10621877—42no—
131#10621877—42no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—41no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43—22no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—42no—
140C23×C43—42no—
141C23×C43—41no—
142C23×C43—41no—
143C23×C43C4×D411yescharacteristic
144C23×C43#12011yescharacteristic
145C23×C43#12111yescharacteristic
146Q8×C43—24no—
147Q8×C43—22no—
148Q8×C43#9914yes—
149D4×C43—22no—
150D4×C43—22no—
151D4×C43—44no—
152D4×C43—44no—
153D4×C43—42no—
154C2×C4×C43—24no—
155C2×C4×C43—22no—
156C2×C4×C43—22no—
157C2×C4×C43—22no—
158C2×C4×C43—22no—
159C2×C4×C43—22no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—44no—
164C2×C4×C43—44no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—42no—
168C2×C4×C43—41no—
169C2×C4×C43—42no—
170C2×C4×C43—41no—
171C2×C4×C43—42no—
172C2×C4×C43—41no—
173C2×C4×C43C2×C22⋊C411yescharacteristic
174C2×C4×C43C4×D411yescharacteristic
175C2×C4×C43#12111yescharacteristic
176C2×C4×C43#12311yescharacteristic
177C2×Dic43—42no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—81no—
181C2×Dic43—81no—
182C2×Dic43—81no—
183C2×Dic43—81no—
184Dic86—42no—
185Dic86—81no—
186C43⋊C8—42no—
187C43⋊C8—81no—
188#9364—431nomaximal, Sylow
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—42no—
198C22×C43—42no—
199C22×C43—42no—
200C22×C43—81no—
201C22×C43—81no—
202C22×C43—82no—
203C22×C43—82no—
204C22×C43#38611yescharacteristic
205C22×C43#45511yescharacteristic
206C22×C43#45611yescharacteristic
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—24no—
210C4×C43—21no—
211C4×C43—42no—
212C4×C43—82no—
213C4×C43—81no—
214C4×C43C2×#9912yes—
215Dic43—82no—
216Dic43—81no—
217Dic43—81no—
218#3007—431no—
219#2341D4311yescharacteristic
220#1996—431no—
221#1789—431no—
222#1508—431no—
223#1305—431no—
224#1297—431no—
225C2×C43—21no—
226C2×C43—21no—
227C2×C43—41no—
228C2×C43—41no—
229C2×C43—82no—
230C2×C43#188211yescharacteristic
231C2×C43#189811yescharacteristic
232C2×C43#190611yescharacteristic
233C22×#41C2×D4311yescharacteristic
234C2×#137—432no—
235C2×C22⋊Q8—431no—
236C2×C4×Q8—21no—
237#452—862no—
238#451—861no—
239#450—861no—
240C2×#104—862no—
241#417—432no—
242#407—431no—
243#407—431no—
244#390—21no—
245#390—22no—
246#380—21no—
247#380C2×D4311yescharacteristic
248C4×C22⋊C4—21no—
249C4×C22⋊C4—431no—
250C4×C22⋊C4C2×D4311yescharacteristic
251#342—862no—
252#328—861no—
253#328—861no—
254C43#936411yescharacteristic, complemented, Sylow
255C2×#41—21no—
256C2×#41—21no—
257C2×#41—44no—
258C2×#41C4×D4312yes—
259C2×#41D17212yes—
260C22×Q8—431no—
261C22×Q8C22⋊D4311yescharacteristic
262C22×D4—21no—
263C22×D4C22⋊D4311yescharacteristic
264C23×C4—21no—
265C23×C4C22×D4311yescharacteristic
266#137—1724no—
267C2×Q16—862no—
268C2×SD16—862no—
269C2×M16—432no—
270C2×M16—861no—
271C22⋊Q8—861no—
272C22⋊Q8—861no—
273C22⋊Q8—861no—
274C22⋊Q8—861no—
275C4×Q8—44no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—431no—
279C2×C4⋊C4—861no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—861no—
284C2×C22⋊C4—861no—
285C2×C22⋊C4C22⋊D4312yes—
286C2×C42—22no—
287C2×C42—21no—
288C2×C42—861no—
289#104—1724no—
290#103—862no—
291#102—862no—
292C22⋊C8—861no—
293C22⋊C8—861no—
294C22⋊C8—861no—
295C22⋊C8—861no—
296#95—21no—
297#95—861no—
298#95C22⋊D4311yescharacteristic
299#95C22⋊D4311yescharacteristic
300C24—21no—
301C24C2×C22⋊D4311yescharacteristic
302#41—24no—
303#41—24no—
304#41—42no—
305#41—42no—
306#41—44no—
307#41—44no—
308C2×Q8—24no—
309C2×Q8—21no—
310C2×Q8—861no—
311C2×Q8—861no—
312C2×Q8—1722no—
313C2×Q8(C2×D43)⋊C412yes—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—21no—
317C2×D4—42no—
318C2×D4—44no—
319C2×D4(C2×D43)⋊C412yes—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—42no—
327C22×C4—44no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—1721no—
331C22×C4C2×C4×D4311yescharacteristic
332C22×C4C2×D17211yescharacteristic
333C22×C4#1062189811yescharacteristic
334C22×C4#1062189811yescharacteristic
335C22×C4C2×C22⋊D4311yescharacteristic
336C22×C4C2×C22⋊D4311yescharacteristic
337Q16—1724no—
338SD16—1724no—
339M16—1722no—
340M16—1722no—
341C2×C8—862no—
342C2×C8—1721no—
343C4⋊C4—44no—
344C4⋊C4—42no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—1721no—
348C4⋊C4—1721no—
349C22⋊C4—42no—
350C22⋊C4—44no—
351C22⋊C4—42no—
352C22⋊C4—82no—
353C22⋊C4—862no—
354C22⋊C4—1721no—
355C22⋊C4—1721no—
356C22⋊C4—1721no—
357C42—44no—
358C42—42no—
359C42—1722no—
360C23—21no—
361C23—21no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—42no—
367C23—41no—
368C23—41no—
369C23C4×C22⋊D4311yescharacteristic
370C23#1306329411yescharacteristic
371C23#1306329911yescharacteristic
372Q8—24no—
373Q8—22no—
374Q8—3441no—
375Q8—1722no—
376Q8#1306323914yes—
377D4—22no—
378D4—22no—
379D4—44no—
380D4—44no—
381D4—42no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—3441no—
402C2×C4—3441no—
403C2×C4—3441no—
404C2×C4—3441no—
405C2×C4—1722no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4C2×(C2×D43)⋊C411yescharacteristic
409C2×C4C4×C22⋊D4311yescharacteristic
410C2×C4#1306329911yescharacteristic
411C2×C4#1306330811yescharacteristic
412C8—3441no—
413C8—1722no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—82no—
428C22—82no—
429C22#1458277811yescharacteristic
430C22#1458307711yescharacteristic
431C22#1458308211yescharacteristic
432C4—21no—
433C4—24no—
434C4—21no—
435C4—21no—
436C4—42no—
437C4—82no—
438C4—81no—
439C4—3442no—
440C4—3441no—
441C4—3441no—
442C4C2×#1306323912yes—
443C2—21no—
444C2—21no—
445C2—41no—
446C2—41no—
447C2—82no—
448C2#1913496411yescharacteristic
449C2#1913504811yescharacteristic
450C2#1913509611yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2341C2
socleC22×C43#386
prime radicalC22×#41×C43C22
cosocleC23×C4×C43C23
hypercenter#2341D43
hypocenterC43#9364
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. #19135579C2semidirect
4. #19133114C2semidirect
5. #19132501C2semidirect
6. #19132481C2semidirect
8. C2×#13063355C4semidirect
14. #14582900C4semidirect
254. C43#9364semidirect

Maximal subgroups

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

subgroupindex
#191438552
#191355792
#191345392
#191331142
#191325012
#191324812
C43×#23412
#936443