Finite Group Databasebeta

← #25014149

Subgroups — #25014149

Order 11008.

694 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C2×#14582883C211yesmaximal, characteristic
2#19138219C211yesmaximal, characteristic
3C2×#14582697C212yesmaximal, complemented
4#19132721C212yesmaximal, complemented
5C43×#1785C211yesmaximal, characteristic
6C22×#10621877—21no—
7C2×#13063323C2211yescharacteristic
8C2×#13063312C411yescharacteristic
9C2×#13063304C411yescharacteristic
10#14582883—24no—
11C2×#13063244C2212yes—
12C2×#13063242—21no—
13#14582813—21no—
14#14582813—21no—
15#14582806C2211yescharacteristic
16#14582802C411yescharacteristic
17#14582772—21no—
18#14582772—21no—
19C4×C22⋊Dic43C411yescharacteristic
20#14582697—24no—
21C22×#41×C43C2211yescharacteristic
22C2×#101×C43C2212yes—
23C2×#100×C43—21no—
24C43×#407—21no—
25C22×Dic86C2×C411yescharacteristic
26C2×#10621877—24no—
27C2×#10621877—22no—
28C2×#10621877—41no—
29C2×#10621877—42no—
30C22×C43⋊C8—41no—
31#13063323—22no—
32#13063323—22no—
33#13063312—42no—
34#13063304—41no—
35#13063304—41no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46C2×C4×Dic43C2×C411yescharacteristic
47C2×C4×Dic43C2×C411yescharacteristic
48#13063244—22no—
49#13063244D414yes—
50#13063242—24no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C2×#41×C43—22no—
55C2×#41×C43—22no—
56C2×#41×C43—41no—
57C2×#41×C43—41no—
58C2×#41×C43—42no—
59C22×Q8×C43C2311yescharacteristic
60C22×D4×C43C2×C411yescharacteristic
61C22×D4×C43D411yescharacteristic
62C22×D4×C43D411yescharacteristic
63C23×C4×C43C2×C411yescharacteristic
64C23×C4×C43D411yescharacteristic
65C23×C4×C43D411yescharacteristic
66C2×M16×C43—22no—
67#101×C43—22no—
68#101×C43—22no—
69#100×C43—42no—
70C22⋊C8×C43—41no—
71C22⋊C8×C43—41no—
72C24×C43C22⋊C411yescharacteristic
73C24×C43C22⋊C411yescharacteristic
74C24×C43C22⋊C411yescharacteristic
75#41×C43—44no—
76#41×C43—44no—
77#41×C43—44no—
78#41×C43—44no—
79C2×Q8×C43—41no—
80C2×Q8×C43—41no—
81C2×Q8×C43C2×D412yes—
82C2×Q8×C43#4112yes—
83C2×D4×C43—22no—
84C2×D4×C43—21no—
85C2×D4×C43—22no—
86C2×D4×C43—21no—
87C2×D4×C43—22no—
88C2×D4×C43—22no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C2×D4×C43—41no—
92C2×D4×C43—41no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—21no—
100C22×C4×C43—21no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—41no—
105C22×C4×C43—41no—
106C22×C4×C43C22⋊C411yescharacteristic
107C22×C4×C43C22×C411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×Dic43—21no—
111C22×Dic43—21no—
112C22×Dic43—21no—
113C22×Dic43—21no—
114C2×Dic86—22no—
115C2×Dic86—41no—
116C2×Dic86—41no—
117M16×C43—42no—
118M16×C43—42no—
119C2×C8×C43—42no—
120C22⋊Dic43—42no—
121C22⋊Dic43—42no—
122C22⋊Dic43—42no—
123C22⋊Dic43—42no—
124C22⋊Dic43—42no—
125C22⋊Dic43—42no—
126C4⋊Dic43—41no—
127Dic43⋊C4—41no—
128Dic43⋊C4—41no—
129Dic43⋊C4—41no—
130Dic43⋊C4—42no—
131Dic43⋊C4—41no—
132C4×Dic43—22no—
133C4×Dic43—41no—
134#10621877—24no—
135#10621877—44no—
136#10621877—42no—
137C2×C43⋊C8—44no—
138C2×C43⋊C8—42no—
139C23×C43—21no—
140C23×C43—21no—
141C23×C43—21no—
142C23×C43—21no—
143C23×C43—21no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—41no—
148C23×C43—41no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43#9912yes—
154C23×C43C2×C22⋊C411yescharacteristic
155Q8×C43—42no—
156Q8×C43—42no—
157D4×C43—44no—
158D4×C43—44no—
159D4×C43—42no—
160D4×C43—42no—
161C2×C4×C43—22no—
162C2×C4×C43—22no—
163C2×C4×C43—22no—
164C2×C4×C43—22no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—21no—
173C2×C4×C43—42no—
174C2×C4×C43—42no—
175C2×C4×C43—42no—
176C2×C4×C43—42no—
177C2×C4×C43#9911yescharacteristic
178C2×C4×C43#9911yescharacteristic
179C2×C4×C43C4×D412yes—
180C2×C4×C43#12011yescharacteristic
181C2×C4×C43#12112yes—
182C2×C4×C43#12311yescharacteristic
183C2×Dic43—22no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—41no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195Dic86—82no—
196C8×C43—82no—
197C43⋊C8—44no—
198#13095—431nomaximal, Sylow
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—22no—
202C22×C43—42no—
203C22×C43—42no—
204C22×C43—41no—
205C22×C43—41no—
206C22×C43—41no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43—41no—
210C22×C43—41no—
211C22×C43—41no—
212C22×C43—81no—
213C22×C43—81no—
214C22×C43—81no—
215C22×C43—81no—
216C22×C43#38611yescharacteristic
217C22×C43C2×#9911yescharacteristic
218C22×C43C2×#9911yescharacteristic
219C4×C43—21no—
220C4×C43—22no—
221C4×C43—22no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225Dic43—42no—
226Dic43—81no—
227Dic43—81no—
228Dic43—81no—
229C2×#413—431no—
230#2432—431no—
231C2×#356—432no—
232#1785D4311yescharacteristic
233#1394—432no—
234C2×C43—21no—
235C2×C43—21no—
236C2×C43—42no—
237C2×C43—81no—
238C2×C43—81no—
239C2×C43#189811yescharacteristic
240C2×C43#213211yescharacteristic
241C2×C43#213511yescharacteristic
242C22×#41C2×D4311yescharacteristic
243C22×M16—861no—
244C2×C4⋊Q8—431no—
245C2×#124—431no—
246C2×C22⋊Q8—431no—
247#413—864no—
248C2×#101—432no—
249C2×#101C2×D4312yes—
250C2×#100—21no—
251C2×#100—861no—
252#407—21no—
253#394—861no—
254#394—861no—
255#391—431no—
256#390—431no—
257#385—861no—
258#385—861no—
259C4×C22⋊C4—431no—
260#356—864no—
261C43#1309511yescharacteristic, complemented, Sylow
262C2×#41—22no—
263C2×#41—22no—
264C2×#41—41no—
265C2×#41—41no—
266C2×#41—42no—
267C22×Q8—431no—
268C22×Q8C22×D4311yescharacteristic
269C22×D4C4×D4311yescharacteristic
270C22×D4D17211yescharacteristic
271C22×D4C22⋊D4311yescharacteristic
272C23×C4C4×D4311yescharacteristic
273C23×C4D17211yescharacteristic
274C23×C4C22⋊D4311yescharacteristic
275C2×M16—22no—
276C2×M16—864no—
277C2×M16—862no—
278C2×M16—1722no—
279C2×M16—1721no—
280C22×C8—1721no—
281C4⋊Q8—862no—
282C4⋊Q8—862no—
283#124—1722no—
284C22⋊Q8—1721no—
285C22⋊Q8—1721no—
286C2×C4⋊C4—431no—
287C2×C4⋊C4—861no—
288C2×C4⋊C4—861no—
289C2×C4⋊C4—861no—
290C2×C22⋊C4—861no—
291C2×C22⋊C4—861no—
292C2×C22⋊C4—861no—
293C2×C22⋊C4—861no—
294C2×C22⋊C4—861no—
295C2×C22⋊C4—861no—
296C2×C42—431no—
297C2×C42—431no—
298#101—22no—
299#101—22no—
300#101—434no—
301#101—862no—
302#100—42no—
303#100—864no—
304C22⋊C8—41no—
305C22⋊C8—41no—
306#95—861no—
307#95—861no—
308#95—861no—
309C24(C2×D43)⋊C411yescharacteristic
310C24(C2×D43)⋊C411yescharacteristic
311C24(C2×D43)⋊C411yescharacteristic
312#41—44no—
313#41—44no—
314#41—44no—
315#41—44no—
316C2×Q8—41no—
317C2×Q8—41no—
318C2×Q8—862no—
319C2×Q8—1721no—
320C2×Q8—1721no—
321C2×Q8D4×D4312yes—
322C2×Q8#1062190012yes—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—21no—
327C2×D4—22no—
328C2×D4—21no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—861no—
347C22×C4—861no—
348C22×C4—861no—
349C22×C4—861no—
350C22×C4(C2×D43)⋊C411yescharacteristic
351C22×C4C2×C4×D4311yescharacteristic
352C22×C4C2×D17211yescharacteristic
353C22×C4C2×C22⋊D4311yescharacteristic
354M16—42no—
355M16—42no—
356M16—864no—
357M16—1724no—
358M16—1722no—
359C2×C8—42no—
360C2×C8—1724no—
361C2×C8—1722no—
362C4⋊C4—1721no—
363C4⋊C4—1721no—
364C4⋊C4—1721no—
365C4⋊C4—1721no—
366C4⋊C4—1722no—
367C4⋊C4—1721no—
368C22⋊C4—1722no—
369C22⋊C4—1722no—
370C22⋊C4—1722no—
371C22⋊C4—1722no—
372C22⋊C4—1722no—
373C22⋊C4—1722no—
374C42—862no—
375C42—1721no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23#1306323912yes—
391C23C2×(C2×D43)⋊C411yescharacteristic
392Q8—42no—
393Q8—42no—
394Q8—3442no—
395D4—44no—
396D4—44no—
397D4—42no—
398D4—42no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—862no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4—1721no—
419C2×C4—1721no—
420C2×C4—1721no—
421C2×C4—1721no—
422C2×C4—1721no—
423C2×C4—1721no—
424C2×C4—1721no—
425C2×C4—1721no—
426C2×C4—1721no—
427C2×C4#1306323911yescharacteristic
428C2×C4#1306323911yescharacteristic
429C2×C4(C22⋊D43)⋊C412yes—
430C2×C4#1306329511yescharacteristic
431C2×C4#1306329712yes—
432C2×C4#1306330911yescharacteristic
433C8—82no—
434C8—1724no—
435C22—21no—
436C22—21no—
437C22—22no—
438C22—42no—
439C22—42no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22#1458277611yescharacteristic
453C22C2×#1306323911yescharacteristic
454C22C2×#1306323911yescharacteristic
455C4—22no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—22no—
461C4—3441no—
462C4—3441no—
463C4—3441no—
464C4—1722no—
465C2—21no—
466C2—21no—
467C2—42no—
468C2—81no—
469C2—81no—
470C2#1913504611yescharacteristic
471C2#1913627811yescharacteristic
472C2#1913628911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC43×#1785C2
socleC22×C43C2×#99
prime radicalC22×#41×C43C22
cosocleC22×Q8×C43C23
hypercenter#1785D43
hypocenterC43#13095
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #1785

Complements

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

NH ≅ G/Ntype
3. C2×#14582697C2semidirect
4. #19132721C2semidirect
261. C43#13095semidirect

Maximal subgroups

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

subgroupindex
C2×#145828832
#191382192
C2×#145826972
#191327212
C43×#17852
#1309543