Finite Group Databasebeta

← #25012835

Subgroups — #25012835

Order 11008.

992 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 992 conjugacy classes of subgroups — too many to draw. Only its 115 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#19134516C211yesmaximal, characteristic
2#19134510C211yesmaximal, characteristic
3#19132713C214yesmaximal, complemented
4C2×C43×#386C211yesmaximal, characteristic
5C2×#13063242—21no—
6C2×#13063242C2212yes—
7C2×#13063240—21no—
8C2×#13063240C2212yes—
9#14582863—21no—
10#14582755—21no—
11C23×D4×C43C2211yescharacteristic
12C24×C4×C43C411yescharacteristic, complemented
13C22×C22⋊C4×C43—21no—
14C22×C22⋊C4×C43C411yescharacteristic, complemented
15C43×#386—21no—
16C43×#386—21no—
17C43×#386C412yescomplemented
18C43×#386C2212yes—
19C2×#95×C43—21no—
20C2×#10621877—22no—
21C2×C22⋊Dic43—22no—
22C2×C22⋊Dic43—41no—
23C2×C22⋊Dic43—41no—
24#13063242—24no—
25#13063242—42no—
26#13063240—24no—
27#13063240—42no—
28C22⋊(C43⋊C8)—41no—
29C22⋊(C43⋊C8)—41no—
30C25×C43C2×C411yescharacteristic
31C25×C43D411yescharacteristic
32C22×D4×C43—24no—
33C22×D4×C43—41no—
34C22×D4×C43—41no—
35C22×D4×C43—42no—
36C22×D4×C43C2×C411yescharacteristic
37C22×D4×C43D411yescharacteristic
38C22×D4×C43D411yescharacteristic
39C22×D4×C43C2311yescharacteristic
40C23×C4×C43—21no—
41C23×C4×C43—21no—
42C23×C4×C43—21no—
43C23×C4×C43—44no—
44C23×C4×C43—41no—
45C23×C4×C43—41no—
46C23×C4×C43C2×C412yes—
47C23×C4×C43D411yescharacteristic
48C2×C22⋊C4×C43—22no—
49C2×C22⋊C4×C43—21no—
50C2×C22⋊C4×C43—22no—
51C2×C22⋊C4×C43—44no—
52C2×C22⋊C4×C43—42no—
53C2×C22⋊C4×C43C2×C412yes—
54#95×C43—22no—
55#95×C43—22no—
56C24×C43—22no—
57C24×C43—21no—
58C24×C43—21no—
59C24×C43—22no—
60C24×C43—22no—
61C24×C43—21no—
62C24×C43—21no—
63C24×C43—41no—
64C24×C43—42no—
65C24×C43—42no—
66C24×C43—42no—
67C24×C43—42no—
68C24×C43C22⋊C411yescharacteristic
69C24×C43C22⋊C411yescharacteristic
70C24×C43C22⋊C411yescharacteristic
71C24×C43C22×C411yescharacteristic
72C24×C43C2×D411yescharacteristic
73C2×D4×C43—22no—
74C2×D4×C43—22no—
75C2×D4×C43—22no—
76C2×D4×C43—22no—
77C2×D4×C43—22no—
78C2×D4×C43—41no—
79C2×D4×C43—41no—
80C2×D4×C43—41no—
81C2×D4×C43—41no—
82C2×D4×C43—41no—
83C2×D4×C43—41no—
84C2×D4×C43—48no—
85C2×D4×C43—48no—
86C2×D4×C43#4114yes—
87C22×C4×C43—24no—
88C22×C4×C43—22no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—22no—
92C22×C4×C43—22no—
93C22×C4×C43—41no—
94C22×C4×C43—42no—
95C22×C4×C43—42no—
96C22×C4×C43—42no—
97C22×C4×C43—42no—
98C22×C4×C43—42no—
99C22×C4×C43—42no—
100C22×C4×C43—44no—
101C22×C4×C43—44no—
102C22×C4×C43—44no—
103C22×C4×C43—48no—
104C22×C4×C43—44no—
105C22×C4×C43—41no—
106C22×C4×C43—41no—
107C22×C4×C43C22⋊C411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×Dic43—42no—
110C22⋊C4×C43—42no—
111C22⋊C4×C43—44no—
112C22⋊C4×C43—44no—
113C22⋊C4×C43—42no—
114C22⋊Dic43—42no—
115C22⋊Dic43—42no—
116C22⋊Dic43—82no—
117C22⋊Dic43—82no—
118#10621877—42no—
119#10621877—42no—
120C2×C43⋊C8—42no—
121C23×C43—22no—
122C23×C43—22no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—24no—
126C23×C43—24no—
127C23×C43—21no—
128C23×C43—21no—
129C23×C43—21no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43—42no—
137C23×C43—42no—
138C23×C43—41no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43—41no—
142C23×C43—42no—
143C23×C43—48no—
144C23×C43—48no—
145C23×C43—42no—
146C23×C43—41no—
147C23×C43—41no—
148C23×C43—41no—
149C23×C43—41no—
150C23×C43—48no—
151C23×C43—42no—
152C23×C43—42no—
153C23×C43—42no—
154C23×C43—42no—
155C23×C43—81no—
156C23×C43—81no—
157C23×C43—84no—
158C23×C43#9911yescharacteristic
159C23×C43#9911yescharacteristic
160C23×C43#9912yes—
161C23×C43C2×C22⋊C411yescharacteristic
162C23×C43#11712yes—
163C23×C43#12312yes—
164D4×C43—44no—
165D4×C43—44no—
166D4×C43—44no—
167D4×C43—44no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—24no—
171C2×C4×C43—21no—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—42no—
175C2×C4×C43—42no—
176C2×C4×C43—42no—
177C2×C4×C43—44no—
178C2×C4×C43—44no—
179C2×C4×C43—48no—
180C2×C4×C43—44no—
181C2×C4×C43—42no—
182C2×C4×C43—44no—
183C2×C4×C43—42no—
184C2×C4×C43—42no—
185C2×C4×C43—42no—
186C2×C4×C43—84no—
187C2×C4×C43#12312yes—
188C2×Dic43—82no—
189C2×Dic43—82no—
190C2×Dic43—82no—
191C43⋊C8—82no—
192#12852—431nomaximal, Sylow
193C22×C43—24no—
194C22×C43—24no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—22no—
202C22×C43—22no—
203C22×C43—22no—
204C22×C43—42no—
205C22×C43—42no—
206C22×C43—42no—
207C22×C43—42no—
208C22×C43—42no—
209C22×C43—48no—
210C22×C43—48no—
211C22×C43—42no—
212C22×C43—41no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43—41no—
216C22×C43—41no—
217C22×C43—41no—
218C22×C43—41no—
219C22×C43—41no—
220C22×C43—41no—
221C22×C43—81no—
222C22×C43—84no—
223C22×C43—84no—
224C22×C43—81no—
225C22×C43AΣL(1,𝔽16)12yes—
226C22×C43#35212yes—
227C22×C43#38111yescharacteristic
228C22×C43C2×#9911yescharacteristic
229C22×C43C2×#9911yescharacteristic
230C4×C43—22no—
231C4×C43—41no—
232C4×C43—44no—
233C4×C43—82no—
234Dic43—162no—
235C2×#386D4311yescharacteristic
236#1783—431no—
237#1781—431no—
238#1390—434no—
239C2×C43—21no—
240C2×C43—21no—
241C2×C43—22no—
242C2×C43—22no—
243C2×C43—42no—
244C2×C43—42no—
245C2×C43—42no—
246C2×C43—81no—
247C2×C43#181911yescharacteristic
248C2×C43C2×AΣL(1,𝔽16)11yescharacteristic
249C2×C43C2×#35211yescharacteristic
250C23×D4C2×D4311yescharacteristic
251C24×C4Dic4311yescharacteristic, complemented
252C22×C22⋊C4—21no—
253C22×C22⋊C4Dic4311yescharacteristic, complemented
254C2×#100—432no—
255C2×#100—861no—
256C2×#99—432no—
257C2×#99—861no—
258#407—861no—
259#386—21no—
260#386—21no—
261#386Dic4312yescomplemented
262#386C2×D4312yes—
263#379—861no—
264C2×#95—21no—
265C43#1285211yescharacteristic, complemented, Sylow
266C25C2×Dic4311yescharacteristic
267C25C22⋊D4311yescharacteristic
268C22×D4—24no—
269C22×D4—41no—
270C22×D4—41no—
271C22×D4—42no—
272C22×D4C2×Dic4311yescharacteristic
273C22×D4C22⋊D4311yescharacteristic
274C22×D4C22⋊D4311yescharacteristic
275C22×D4C22×D4311yescharacteristic
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—44no—
280C23×C4—41no—
281C23×C4—41no—
282C23×C4C2×Dic4312yes—
283C23×C4C22⋊D4311yescharacteristic
284C2×M16—862no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—44no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—862no—
291C2×C22⋊C4—1721no—
292C2×C22⋊C4—1721no—
293C2×C22⋊C4C2×Dic4312yes—
294#100—864no—
295#100—1722no—
296#99—864no—
297#99—1722no—
298C22⋊C8—1721no—
299C22⋊C8—1721no—
300#95—22no—
301#95—22no—
302C24—22no—
303C24—21no—
304C24—21no—
305C24—22no—
306C24—22no—
307C24—21no—
308C24—21no—
309C24—41no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24—42no—
314C24C22⋊Dic4311yescharacteristic
315C24C22⋊Dic4311yescharacteristic
316C24C22⋊Dic4311yescharacteristic
317C24C22×Dic4311yescharacteristic
318C24C2×C22⋊D4311yescharacteristic
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—48no—
331C2×D4—48no—
332C2×D4#1062189814yes—
333C22×C4—24no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—41no—
340C22×C4—44no—
341C22×C4—44no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—48no—
345C22×C4—44no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—42no—
349C22×C4—44no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—1722no—
354C22×C4C22⋊Dic4311yescharacteristic
355C22×C4C2×C22⋊D4311yescharacteristic
356M16—1722no—
357M16—1722no—
358C2×C8—1722no—
359C22⋊C4—44no—
360C22⋊C4—44no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—3442no—
364C22⋊C4—3442no—
365C22⋊C4—1722no—
366C22⋊C4—1722no—
367C23—21no—
368C23—22no—
369C23—22no—
370C23—21no—
371C23—24no—
372C23—24no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—42no—
383C23—42no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—42no—
389C23—48no—
390C23—48no—
391C23—42no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—48no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23—81no—
402C23—81no—
403C23—84no—
404C23#1306324011yescharacteristic
405C23#1306324011yescharacteristic
406C23#1306324012yes—
407C23C2×C22⋊Dic4311yescharacteristic
408C23#1306328412yes—
409C23#1306330812yes—
410D4—44no—
411D4—44no—
412D4—44no—
413D4—44no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—24no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—48no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—84no—
433C2×C4—3442no—
434C2×C4—3442no—
435C2×C4—3442no—
436C2×C4#1306330812yes—
437C8—3442no—
438C22—24no—
439C22—24no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—48no—
455C22—48no—
456C22—42no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—81no—
467C22—84no—
468C22—84no—
469C22—81no—
470C22#1458268612yes—
471C22#1458268912yes—
472C22#1458276211yescharacteristic
473C22C2×#1306324011yescharacteristic
474C22C2×#1306324011yescharacteristic
475C4—22no—
476C4—41no—
477C4—44no—
478C4—82no—
479C4—6882no—
480C2—21no—
481C2—21no—
482C2—22no—
483C2—22no—
484C2—42no—
485C2—42no—
486C2—42no—
487C2—81no—
488C2#1913466911yescharacteristic
489C2C2×#1458268611yescharacteristic
490C2C2×#1458268911yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC24×C43C22×C4
FrattiniC22×D4C22×D43
FittingC2×C43×#386C2
socleC22×C43C2×#99
prime radicalC23×D4×C43C22
cosocleC22×D4×C43C23
hypercenterC2×#386D43
hypocenterC43#12852
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. #19132713C2semidirect
12. C24×C4×C43C4semidirect
14. C22×C22⋊C4×C43C4semidirect
17. C43×#386C4semidirect
251. C24×C4Dic43semidirect
253. C22×C22⋊C4Dic43semidirect
261. #386Dic43semidirect
265. C43#12852semidirect

Maximal subgroups

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

subgroupindex
#191345162
#191345102
#191327132
C2×C43×#3862
#1285243