Finite Group Databasebeta

← #24988123

Subgroups — #24988123

Order 11008.

720 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 720 conjugacy classes of subgroups — too many to draw. Only its 135 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#19134361C211yesmaximal, characteristic, complemented
2#19133215C212yesmaximal, complemented
3#19133055C212yesmaximal, complemented
4#19132929C211yesmaximal, characteristic, complemented
5C43×#3493C211yesmaximal, characteristic
6#14582956C2212yes—
7C2×C22⋊(C43⋊C8)—21no—
8C2×#13063236C2211yescharacteristic
9C2×C4×C43⋊C8C2211yescharacteristic
10#14582654—21no—
11#14582641—22no—
12#14582639—22no—
13Q8⋊(C43⋊C8)—22no—
14D4⋊(C43⋊C8)—22no—
15#14582625—21no—
16#14582623—21no—
17C43×#556—22no—
18C43×#555—22no—
19C43×#553—22no—
20C43×#552—22no—
21C43×#544C411yescharacteristic
22C43×#538—21no—
23C43×#538C412yes—
24C43×#537C411yescharacteristic
25C43×#529—21no—
26C43×#529C2212yes—
27C43×#525—21no—
28C43×#520—21no—
29C2×#117×C43C2211yescharacteristic
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32C4⋊(C43⋊C8)—22no—
33C22⋊(C43⋊C8)—24no—
34C22⋊(C43⋊C8)—22no—
35#13063236—22no—
36#13063236—22no—
37C4×C43⋊C8—22no—
38C2×#41×C43—21no—
39C23×C4×C43D411yescharacteristic
40C4⋊Q8×C43—22no—
41#126×C43—22no—
42#126×C43—22no—
43#126×C43—22no—
44#126×C43—22no—
45#125×C43—21no—
46#125×C43—22no—
47#125×C43D412yes—
48#124×C43—21no—
49#124×C43—22no—
50#124×C43—22no—
51#124×C43D412yes—
52#123×C43—22no—
53#123×C43—22no—
54#123×C43—22no—
55C22⋊Q8×C43—21no—
56C22⋊Q8×C43—21no—
57C22⋊Q8×C43—21no—
58C22⋊Q8×C43—22no—
59C22⋊Q8×C43C2×C412yes—
60#121×C43—21no—
61#121×C43—21no—
62#121×C43—22no—
63#121×C43—22no—
64#121×C43—22no—
65#121×C43—21no—
66#121×C43C2×C412yes—
67#120×C43—22no—
68C4×Q8×C43—22no—
69C4×Q8×C43—21no—
70C4×Q8×C43D412yes—
71C4×D4×C43—22no—
72C4×D4×C43—22no—
73C4×D4×C43—22no—
74C4×D4×C43—21no—
75C4×D4×C43—22no—
76C4×D4×C43—22no—
77C4×D4×C43D412yes—
78#117×C43—22no—
79#117×C43—22no—
80#117×C43—21no—
81#117×C43—22no—
82#117×C43—22no—
83#117×C43—22no—
84C2×C4⋊C4×C43—22no—
85C2×C4⋊C4×C43C2×C411yescharacteristic
86C2×C4⋊C4×C43D411yescharacteristic
87C2×C22⋊C4×C43C2×C411yescharacteristic
88C2×C22⋊C4×C43D411yescharacteristic
89C2×C42×C43D411yescharacteristic
90C2×C42×C43C2311yescharacteristic
91C24×C43C22⋊C411yescharacteristic
92#41×C43—42no—
93#41×C43—42no—
94C2×Q8×C43—21no—
95C2×Q8×C43—21no—
96C2×Q8×C43C22⋊C412yes—
97C2×D4×C43—21no—
98C2×D4×C43—22no—
99C2×D4×C43—22no—
100C2×D4×C43—21no—
101C2×D4×C43—22no—
102C2×D4×C43C22⋊C412yes—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—22no—
109C22×C4×C43—41no—
110C22×C4×C43C22⋊C411yescharacteristic
111C22×C4×C43C22⋊C411yescharacteristic
112C22×C4×C43C22⋊C411yescharacteristic
113C22×C4×C43C22×C411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C4⋊C4×C43—21no—
117C4⋊C4×C43—22no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—22no—
120C4⋊C4×C43—21no—
121C4⋊C4×C43—21no—
122C4⋊C4×C43—22no—
123C4⋊C4×C43—22no—
124C4⋊C4×C43—22no—
125C4⋊C4×C43—22no—
126C4⋊C4×C43—22no—
127C4⋊C4×C43—22no—
128C4⋊C4×C43C22⋊C412yes—
129C4⋊C4×C43C22⋊C412yes—
130C22⋊C4×C43—22no—
131C22⋊C4×C43—22no—
132C22⋊C4×C43—22no—
133C22⋊C4×C43—22no—
134C22⋊C4×C43—22no—
135C22⋊C4×C43—22no—
136C22⋊C4×C43—22no—
137C22⋊C4×C43—22no—
138C22⋊C4×C43—22no—
139C22⋊C4×C43—22no—
140C22⋊C4×C43—22no—
141C42×C43—22no—
142C42×C43—22no—
143C42×C43—21no—
144C42×C43—21no—
145C42×C43—22no—
146C42×C43C2×D412yes—
147C42×C43C2×D412yes—
148C2×C43⋊C8—22no—
149C2×C43⋊C8—22no—
150C2×C43⋊C8—41no—
151C2×C43⋊C8—41no—
152C2×C43⋊C8—41no—
153C2×C43⋊C8—41no—
154C2×C43⋊C8—42no—
155C23×C43—21no—
156C23×C43—22no—
157C23×C43—21no—
158C23×C43—21no—
159C23×C43—41no—
160C23×C43—41no—
161C23×C43C2×C22⋊C411yescharacteristic
162Q8×C43—42no—
163Q8×C43—42no—
164Q8×C43—81no—
165D4×C43—42no—
166D4×C43—42no—
167D4×C43—42no—
168D4×C43—42no—
169D4×C43—82no—
170D4×C43—81no—
171D4×C43—82no—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—21no—
175C2×C4×C43—21no—
176C2×C4×C43—21no—
177C2×C4×C43—22no—
178C2×C4×C43—21no—
179C2×C4×C43—22no—
180C2×C4×C43—22no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—42no—
184C2×C4×C43—42no—
185C2×C4×C43—44no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—82no—
189C2×C4×C43—82no—
190C2×C4×C43#10412yes—
191C2×C4×C43C2×C22⋊C412yes—
192C2×C4×C43#12012yes—
193C2×C4×C43#12011yescharacteristic
194C2×C4×C43#12011yescharacteristic
195C43⋊C8—42no—
196C43⋊C8—42no—
197C43⋊C8—82no—
198#8349—431nomaximal, Sylow
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—42no—
202C22×C43—41no—
203C22×C43—42no—
204C22×C43—41no—
205C22×C43—42no—
206C22×C43—41no—
207C22×C43—42no—
208C22×C43—81no—
209C22×C43#37911yescharacteristic
210C22×C43C2×#10411yescharacteristic
211C22×C43#42111yescharacteristic
212C4×C43—22no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—22no—
216C4×C43—22no—
217C4×C43—41no—
218C4×C43—42no—
219C4×C43—42no—
220C4×C43—41no—
221C4×C43—42no—
222#3493D4311yescharacteristic
223#1750—431no—
224#1532—432no—
225#1494—432no—
226#1464—431no—
227C2×C43—21no—
228C2×C43—21no—
229C2×C43—82no—
230C2×C43—81no—
231C2×C43#178911yescharacteristic
232C2×C43#179111yescharacteristic
233C2×C43#179411yescharacteristic
234#556—22no—
235#555—22no—
236#553—22no—
237#552—22no—
238#544Dic4311yescharacteristic
239#538—21no—
240#538Dic4312yes—
241#537Dic4311yescharacteristic
242#529—21no—
243#529C2×D4312yes—
244#525—21no—
245#520—21no—
246C2×#117C2×D4311yescharacteristic
247#432—432no—
248C2×C22⋊C8—861no—
249C2×#97—431no—
250C2×C4×C8—431no—
251#336—861no—
252#330—862no—
253#329—862no—
254Q8⋊C8—862no—
255D4⋊C8—862no—
256#324—861no—
257#323—861no—
258C43#834911yescharacteristic, complemented, Sylow
259C2×#41—21no—
260C23×C4C22⋊D4311yescharacteristic
261C22×C8—861no—
262C22×C8—861no—
263C4⋊Q8—22no—
264#126—22no—
265#126—22no—
266#126—22no—
267#126—22no—
268#125—21no—
269#125—22no—
270#125C22⋊D4312yes—
271#124—21no—
272#124—22no—
273#124—22no—
274#124C22⋊D4312yes—
275#123—22no—
276#123—22no—
277#123—22no—
278C22⋊Q8—21no—
279C22⋊Q8—21no—
280C22⋊Q8—21no—
281C22⋊Q8—22no—
282C22⋊Q8C2×Dic4312yes—
283#121—21no—
284#121—21no—
285#121—22no—
286#121—22no—
287#121—22no—
288#121—21no—
289#121C2×Dic4312yes—
290#120—22no—
291C4×Q8—22no—
292C4×Q8—21no—
293C4×Q8C22⋊D4312yes—
294C4×D4—22no—
295C4×D4—22no—
296C4×D4—22no—
297C4×D4—21no—
298C4×D4—22no—
299C4×D4—22no—
300C4×D4C22⋊D4312yes—
301#117—22no—
302#117—22no—
303#117—21no—
304#117—22no—
305#117—22no—
306#117—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4C2×Dic4311yescharacteristic
309C2×C4⋊C4C22⋊D4311yescharacteristic
310C2×C22⋊C4C2×Dic4311yescharacteristic
311C2×C22⋊C4C22⋊D4311yescharacteristic
312C2×C42C22⋊D4311yescharacteristic
313C2×C42C22×D4311yescharacteristic
314C4⋊C8—862no—
315C22⋊C8—864no—
316C22⋊C8—862no—
317#97—862no—
318#97—862no—
319C4×C8—862no—
320C24C22⋊Dic4311yescharacteristic
321#41—42no—
322#41—42no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8C22⋊Dic4312yes—
326C2×D4—21no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—21no—
331C2×D4C22⋊Dic4312yes—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4C22⋊Dic4311yescharacteristic
340C22×C4C22⋊Dic4311yescharacteristic
341C22×C4C22⋊Dic4311yescharacteristic
342C22×C4C22×Dic4311yescharacteristic
343C22×C4C2×C22⋊D4311yescharacteristic
344C22×C4C2×C22⋊D4311yescharacteristic
345C2×C8—862no—
346C2×C8—862no—
347C2×C8—1722no—
348C2×C8—1721no—
349C2×C8—1721no—
350C2×C8—1721no—
351C2×C8—1721no—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4C22⋊Dic4312yes—
365C4⋊C4C22⋊Dic4312yes—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—22no—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C22⋊C4—22no—
372C22⋊C4—22no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C42—22no—
378C42—22no—
379C42—21no—
380C42—21no—
381C42—22no—
382C42C2×C22⋊D4312yes—
383C42C2×C22⋊D4312yes—
384C23—21no—
385C23—21no—
386C23—22no—
387C23—21no—
388C23—41no—
389C23—41no—
390C23C2×C22⋊Dic4311yescharacteristic
391Q8—42no—
392Q8—42no—
393Q8—81no—
394D4—42no—
395D4—42no—
396D4—42no—
397D4—42no—
398D4—81no—
399D4—82no—
400D4—82no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4#1306325212yes—
420C2×C4C2×C22⋊Dic4312yes—
421C2×C4#1306329411yescharacteristic
422C2×C4#1306329411yescharacteristic
423C2×C4#1306329412yes—
424C8—3442no—
425C8—1722no—
426C8—1722no—
427C22—21no—
428C22—21no—
429C22—42no—
430C22—41no—
431C22—42no—
432C22—42no—
433C22—41no—
434C22—42no—
435C22—41no—
436C22—81no—
437C22#1458275511yescharacteristic
438C22C2×#1306325211yescharacteristic
439C22#1458291611yescharacteristic
440C4—21no—
441C4—21no—
442C4—22no—
443C4—22no—
444C4—22no—
445C4—42no—
446C4—41no—
447C4—42no—
448C4—41no—
449C4—42no—
450C2—21no—
451C2—21no—
452C2—81no—
453C2—82no—
454C2#1913453911yescharacteristic
455C2#1913454611yescharacteristic
456C2#1913455911yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3493C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3493D43
hypocenterC43#8349
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3493

Complements

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

NH ≅ G/Ntype
1. #19134361C2semidirect
2. #19133215C2semidirect
3. #19133055C2semidirect
4. #19132929C2semidirect
258. C43#8349semidirect

Maximal subgroups

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

subgroupindex
#191343612
#191332152
#191330552
#191329292
C43×#34932
#834943