Finite Group Databasebeta

← #99580

Subgroups — #99580

Order 512.

624 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22287C211yesmaximal, characteristic
2C4×#451C211yesmaximal, characteristic
3#11380C211yesmaximal, characteristic
4#8311C211yesmaximal, characteristic
5#7566C211yesmaximal, characteristic
6#7029C211yesmaximal, characteristic
7#7016C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#451C411yescharacteristic
10C2×C4×Q16—21no—
11C4×C22⋊Q8C2211yescharacteristic
12#1984—21no—
13#1939—21no—
14#1916—21no—
15#1916—21no—
16#1878—21no—
17#1872C411yescharacteristic
18#1863—21no—
19#1852C411yescharacteristic
20#1850—21no—
21#1797C2211yescharacteristic
22#1787C411yescharacteristic
23C4×#103—21no—
24C8×C22⋊C4—21no—
25C4×C22⋊C8C2211yescharacteristic
26C4×C22⋊C8C2211yescharacteristic
27C2×#336—21no—
28C2×#336—21no—
29C2×#336C2211yescharacteristic
30C2×#336C2211yescharacteristic
31C2×Q8⋊C8—21no—
32C2×Q8⋊C8—21no—
33#1272—21no—
34#1271—21no—
35C23×Q8C2×C411yescharacteristic
36C22×Q16—21no—
37C23×C8—21no—
38C23×C8D411yescharacteristic
39C23×C8D411yescharacteristic
40C2×C22⋊Q8C2×C411yescharacteristic
41C2×C4×Q8—21no—
42C2×C4×Q8—21no—
43C2×C4×Q8—21no—
44C2×C4×Q8—21no—
45C2×C4×Q8—42no—
46C2×C4×Q8—42no—
47C2×C4×Q8D411yescharacteristic
48C22×C4⋊C4—21no—
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C42—21no—
51C22×C42C2311yescharacteristic
52#451—22no—
53#451C814yescomplemented
54C4×Q16—42no—
55C4×Q16—42no—
56C2×#107—21no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×C4⋊C8D411yescharacteristic
60C2×C4⋊C8D411yescharacteristic
61C2×#103—21no—
62C2×#103—21no—
63C2×#103—21no—
64C2×#103—21no—
65C2×C22⋊C8—21no—
66C2×C22⋊C8—21no—
67C2×C22⋊C8C2×C411yescharacteristic
68C2×C22⋊C8C2×C411yescharacteristic
69C2×C4×C8—21no—
70C2×C4×C8—21no—
71C2×C4×C8—21no—
72C2×C4×C8—21no—
73#391D411yescharacteristic
74#389D411yescharacteristic
75#387—21no—
76#385—21no—
77#380C2×C411yescharacteristic
78C4×C4⋊C4—21no—
79C4×C4⋊C4D411yescharacteristic
80C4×C22⋊C4—21no—
81#340—21no—
82#340—21no—
83#336—21no—
84#336—21no—
85#336—21no—
86#336—21no—
87#336—21no—
88#336—21no—
89#336—21no—
90#336—21no—
91#336—21no—
92#336—21no—
93#336—21no—
94#336—42no—
95#336—42no—
96Q8⋊C8—42no—
97Q8⋊C8—42no—
98C22×Q8—21no—
99C22×Q8—21no—
100C22×Q8—21no—
101C22×Q8—21no—
102C22×Q8—21no—
103C22×Q8—42no—
104C22×Q8—42no—
105C22×Q8C22⋊C411yescharacteristic
106C22×Q8C2×C812yes—
107C23×C4—21no—
108C23×C4—21no—
109C23×C4C22×C411yescharacteristic
110C23×C4C2×D411yescharacteristic
111C23×C4#4111yescharacteristic
112C2×Q16—24no—
113C2×Q16—42no—
114C2×Q16—42no—
115C22×C8—21no—
116C22×C8—21no—
117C22×C8—21no—
118C22×C8—22no—
119C22×C8—21no—
120C22×C8—21no—
121C22×C8—21no—
122C22×C8—21no—
123C22×C8—21no—
124C22×C8—21no—
125C22×C8—41no—
126C22×C8—41no—
127C22×C8—41no—
128C22×C8—41no—
129C22×C8—41no—
130C22×C8—41no—
131C22×C8—41no—
132C22×C8—41no—
133C22×C8—41no—
134C22×C8—41no—
135C22×C8—41no—
136C22×C8Q1612yescomplemented
137C22⋊Q8—21no—
138C22⋊Q8—21no—
139C22⋊Q8C2×C812yes—
140C22⋊Q8M1612yes—
141C4×Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—41no—
146C4×Q8—41no—
147C4×Q8—41no—
148C4×Q8—41no—
149C4×Q8—41no—
150C4×Q8—41no—
151C4×Q8—42no—
152C4×Q8—42no—
153C4×Q8—42no—
154C4×Q8—42no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—42no—
161C2×C4⋊C4—42no—
162C2×C4⋊C4—42no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4C22⋊C411yescharacteristic
166C2×C4⋊C4C22⋊C411yescharacteristic
167C2×C4⋊C4C22⋊C411yescharacteristic
168C2×C22⋊C4—21no—
169C2×C22⋊C4—21no—
170C2×C42—22no—
171C2×C42—22no—
172C2×C42—21no—
173C2×C42—21no—
174C2×C42—41no—
175C2×C42—41no—
176C2×C42—41no—
177C2×C42—41no—
178C2×C42—41no—
179C2×C42—41no—
180C2×C42C2×D411yescharacteristic
181C2×C42C2×D411yescharacteristic
182C2×C42C2×D411yescharacteristic
183C2×C42#4111yescharacteristic
184#107—42no—
185C4⋊C8—41no—
186C4⋊C8—41no—
187C4⋊C8—81no—
188C4⋊C8—81no—
189#103—24no—
190#103—42no—
191#103—42no—
192#103—42no—
193C22⋊C8—21no—
194C22⋊C8—22no—
195C22⋊C8—21no—
196C22⋊C8—21no—
197C22⋊C8—41no—
198C22⋊C8—41no—
199C22⋊C8—41no—
200C22⋊C8C2×C812yes—
201C4×C8—41no—
202C4×C8—41no—
203C4×C8—41no—
204C4×C8—41no—
205C4×C8—81no—
206C4×C8—81no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212C24C4×D411yescharacteristic
213C2×Q8—21no—
214C2×Q8—22no—
215C2×Q8—22no—
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—22no—
219C2×Q8—22no—
220C2×Q8—44no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×Q8—44no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—44no—
229C2×Q8—44no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8C22⋊C812yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4C2×C22⋊C411yescharacteristic
262C22×C4C4×D411yescharacteristic
263C22×C4#12011yescharacteristic
264C22×C4#12111yescharacteristic
265C22×C4#12111yescharacteristic
266C22×C4#12311yescharacteristic
267C22×C4C22×C811yescharacteristic
268C22×C4C2×M1611yescharacteristic
269C22×C4#13111yescharacteristic
270C22×C4#13111yescharacteristic
271C22×C4C2×Q1611yescharacteristic
272C22×C4#13511yescharacteristic
273C22×C4#13711yescharacteristic
274C22×C4#13711yescharacteristic
275Q16—48no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—42no—
283C2×C8—41no—
284C2×C8—42no—
285C2×C8—41no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—81no—
301C2×C8—81no—
302C2×C8—81no—
303C2×C8—81no—
304C2×C8—81no—
305C2×C8—81no—
306C2×C8—81no—
307C2×C8—81no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4—42no—
320C4⋊C4—42no—
321C4⋊C4—81no—
322C4⋊C4—81no—
323C4⋊C4C22⋊C812yes—
324C22⋊C4—22no—
325C22⋊C4—22no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—21no—
332C42—41no—
333C42—41no—
334C42—42no—
335C42—42no—
336C42—41no—
337C42—41no—
338C42—41no—
339C42—41no—
340C42—42no—
341C42—42no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23#38611yescharacteristic
347C23C8×D411yescharacteristic
348C23#43511yescharacteristic
349C23C4×Q1611yescharacteristic
350C23#44111yescharacteristic
351C23#44311yescharacteristic
352C23#44411yescharacteristic
353Q8—24no—
354Q8—24no—
355Q8—42no—
356Q8—42no—
357Q8—42no—
358Q8—42no—
359Q8—42no—
360Q8—42no—
361Q8—42no—
362Q8—81no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4C2×C22⋊C811yescharacteristic
416C2×C4#40811yescharacteristic
417C2×C4C8×D411yescharacteristic
418C2×C4#43511yescharacteristic
419C2×C4#45111yescharacteristic
420C2×C4#45211yescharacteristic
421C2×C4#45511yescharacteristic
422C2×C4#45611yescharacteristic
423C2×C4B(4,𝔽2)11yescharacteristic
424C2×C4B(4,𝔽2)11yescharacteristic
425C2×C4#46211yescharacteristic
426C2×C4#46411yescharacteristic
427C8—42no—
428C8—42no—
429C8—81no—
430C8—82no—
431C8—82no—
432C8—81no—
433C8—81no—
434C8—81no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22C8×Q1611yescharacteristic
448C22#157911yescharacteristic
449C22#158411yescharacteristic
450C22#158711yescharacteristic
451C22#186911yescharacteristic
452C22#187611yescharacteristic
453C22#187811yescharacteristic
454C22#188111yescharacteristic
455C22#188211yescharacteristic
456C22#188911yescharacteristic
457C22#189111yescharacteristic
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—44no—
465C4—42no—
466C4—41no—
467C4—41no—
468C4—42no—
469C4—81no—
470C4—82no—
471C4—81no—
472C4#160211yescharacteristic
473C4#160311yescharacteristic
474C4#160511yescharacteristic
475C4#160611yescharacteristic
476C2—21no—
477C2—21no—
478C2—21no—
479C2—21no—
480C2#894611yescharacteristic
481C2#895311yescharacteristic
482C2#896511yescharacteristic
483C2#903711yescharacteristic
484C2#904011yescharacteristic
485C2#904811yescharacteristic
486C2#905111yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC22×C4C22×C8
Frattini, cosocleC22×C42C23
socleC23#386
prime radicalC24C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
53. #451C8semidirect
136. C22×C8Q16semidirect

Maximal subgroups

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

subgroupindex
#222872
C4×#4512
#113802
#83112
#75662
#70292
#70162