Finite Group Databasebeta

← #103377

Subgroups — #103377

Order 512.

915 conjugacy classes of subgroups.

The subgroup lattice has 505 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2043C211yesmaximal, characteristic, complemented
2C2×#2023C211yesmaximal, characteristic
3#17071C211yesmaximal, characteristic
4#11384C211yesmaximal, characteristic, complemented
5C2×#1271C211yesmaximal, characteristic, complemented
6C2×#1270C211yesmaximal, characteristic
7#7025C211yesmaximal, characteristic, complemented
8C22×C4⋊Q8C2211yescharacteristic
9C22×#103—21no—
10C22×#103—21no—
11C22×#102—21no—
12C2×#399—21no—
13C2×#396—22no—
14C2×#390C2211yescharacteristic
15C2×#389C2211yescharacteristic
16#2043—22no—
17#2043—22no—
18#2023—22no—
19#2023—22no—
20C2×#340—21no—
21C2×#340—22no—
22C2×#336C2211yescharacteristic
23C2×#336C2211yescharacteristic
24C2×#336C2211yescharacteristic
25#1444—21no—
26#1439—21no—
27#1438—21no—
28C4⋊#95C2211yescharacteristic
29#1271—22no—
30#1270—22no—
31C23×Q8—21no—
32C23×D4D411yescharacteristic
33C23×C8—21no—
34C23×C8—21no—
35C23×C8—21no—
36C2×C4⋊Q8—21no—
37C2×C4⋊Q8—21no—
38C2×C4⋊Q8—21no—
39C2×C4⋊Q8—44no—
40C2×C4⋊Q8D412yes—
41C22×C4⋊C4—21no—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—22no—
45C22×C4⋊C4D411yescharacteristic
46C22×C4⋊C4D411yescharacteristic
47C22×C4⋊C4D411yescharacteristic
48C22×C4⋊C4D412yes—
49C22×C22⋊C4—21no—
50C22×C22⋊C4—21no—
51C22×C22⋊C4—22no—
52C22×C22⋊C4—22no—
53C22×C42C2311yescharacteristic
54C2×#103—24no—
55C2×#103—24no—
56C2×#103—42no—
57C2×#103—44no—
58C2×#103—42no—
59C2×#102—24no—
60C2×#102—44no—
61#399—42no—
62#399—42no—
63#396—44no—
64#396—44no—
65#390—21no—
66#390—21no—
67#390—21no—
68#390—21no—
69#389—21no—
70#389—21no—
71#389—21no—
72#389—21no—
73C2×#95—22no—
74C2×#95—21no—
75C2×#95—21no—
76C2×#95—21no—
77#340—24no—
78#340—44no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336D412yes—
84#336D412yes—
85C25—21no—
86C22×Q8—24no—
87C22×Q8—22no—
88C22×Q8—42no—
89C22×Q8—42no—
90C22×Q8—42no—
91C22×Q8—41no—
92C22×Q8—41no—
93C22×Q8—41no—
94C22×Q8—41no—
95C22×Q8—41no—
96C22×D4—21no—
97C22×D4—21no—
98C22×D4—21no—
99C22×D4—21no—
100C22×D4—21no—
101C22×D4—42no—
102C22×D4—42no—
103C22×D4Q1612yes—
104C23×C4—21no—
105C23×C4—22no—
106C23×C4—21no—
107C23×C4—21no—
108C23×C4—41no—
109C23×C4C2×D411yescharacteristic
110C23×C4C2×D411yescharacteristic
111C23×C4C2×D411yescharacteristic
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—42no—
116C22×C8—41no—
117C22×C8—42no—
118C22×C8—42no—
119C22×C8—42no—
120C22×C8—42no—
121C22×C8—41no—
122C22×C8—41no—
123C22×C8—41no—
124C22×C8—42no—
125C22×C8—41no—
126C22×C8—41no—
127C4⋊Q8—44no—
128C4⋊Q8—44no—
129C4⋊Q8—44no—
130C4⋊Q8—44no—
131C2×C4⋊C4—24no—
132C2×C4⋊C4—24no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—42no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—42no—
150C2×C4⋊C4—42no—
151C2×C4⋊C4—42no—
152C2×C4⋊C4—42no—
153C2×C4⋊C4—44no—
154C2×C4⋊C4—44no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—42no—
158C2×C4⋊C4—42no—
159C2×C4⋊C4—82no—
160C2×C4⋊C4D812yes—
161C2×C4⋊C4SD1614yes—
162C2×C22⋊C4—44no—
163C2×C22⋊C4—44no—
164C2×C22⋊C4—44no—
165C2×C22⋊C4—41no—
166C2×C22⋊C4—41no—
167C2×C22⋊C4—41no—
168C2×C22⋊C4—41no—
169C2×C22⋊C4—41no—
170C2×C22⋊C4—42no—
171C2×C22⋊C4—41no—
172C2×C22⋊C4—41no—
173C2×C22⋊C4—42no—
174C2×C22⋊C4—41no—
175C2×C22⋊C4—82no—
176C2×C22⋊C4—82no—
177C2×C22⋊C4—82no—
178C2×C42—42no—
179C2×C42C2×D411yescharacteristic
180C2×C42C2×D411yescharacteristic
181C2×C42C2×D411yescharacteristic
182C2×C42#4111yescharacteristic
183#103—48no—
184#103—48no—
185#102—48no—
186#95—44no—
187#95—41no—
188#95—41no—
189#95—41no—
190#95—41no—
191#95—41no—
192#95—41no—
193C24—22no—
194C24—41no—
195C24—41no—
196C24—41no—
197C24—42no—
198C24—41no—
199C24—42no—
200C24—41no—
201C24—42no—
202C24—41no—
203C24—42no—
204C24#12011yescharacteristic
205C2×Q8—24no—
206C2×Q8—42no—
207C2×Q8—44no—
208C2×Q8—44no—
209C2×Q8—44no—
210C2×Q8—44no—
211C2×Q8—44no—
212C2×Q8—42no—
213C2×Q8—42no—
214C2×Q8—42no—
215C2×Q8—42no—
216C2×Q8—82no—
217C2×Q8—82no—
218C2×Q8—82no—
219C2×Q8—82no—
220C2×Q8—82no—
221C2×Q8—81no—
222C2×Q8—81no—
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—44no—
226C2×D4—42no—
227C2×D4—44no—
228C2×D4—42no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—82no—
232C2×D4—82no—
233C2×D4—81no—
234C2×D4—81no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—41no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—41no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—44no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—41no—
263C22×C4—42no—
264C22×C4—41no—
265C22×C4—42no—
266C22×C4—81no—
267C22×C4—81no—
268C22×C4—82no—
269C22×C4#12011yescharacteristic
270C22×C4#12011yescharacteristic
271C22×C4#12111yescharacteristic
272C22×C4#12111yescharacteristic
273C22×C4#12111yescharacteristic
274C22×C4#12711yescharacteristic
275C22×C4C2×D811yescharacteristic
276C22×C4C2×SD1612yes—
277C22×C4C2×Q1611yescharacteristic
278C22×C4#13511yescharacteristic
279C22×C4#13511yescharacteristic
280C22×C4AGL(1,ℤ/8)11yescharacteristic
281C22×C4AGL(1,ℤ/8)11yescharacteristic
282C22×C4AGL(1,ℤ/8)12yes—
283C22×C4#13711yescharacteristic
284C22×C4#13711yescharacteristic
285C2×C8—42no—
286C2×C8—42no—
287C2×C8—44no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—82no—
294C2×C8—82no—
295C2×C8—82no—
296C2×C8—82no—
297C2×C8—82no—
298C2×C8—81no—
299C2×C8—81no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—44no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—44no—
308C4⋊C4—44no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—82no—
314C4⋊C4—81no—
315C4⋊C4—81no—
316C4⋊C4—88no—
317C4⋊C4—82no—
318C4⋊C4—81no—
319C4⋊C4—81no—
320C22⋊C4—88no—
321C22⋊C4—88no—
322C22⋊C4—81no—
323C22⋊C4—81no—
324C22⋊C4—82no—
325C22⋊C4—81no—
326C22⋊C4—81no—
327C22⋊C4—81no—
328C22⋊C4—81no—
329C42—41no—
330C42—41no—
331C42—41no—
332C42—41no—
333C23—44no—
334C23—44no—
335C23—42no—
336C23—42no—
337C23—42no—
338C23—82no—
339C23—82no—
340C23—82no—
341C23—82no—
342C23—82no—
343C23—82no—
344C23—82no—
345C23—81no—
346C23—82no—
347C23—81no—
348C23—82no—
349C23—82no—
350C23—81no—
351C23—81no—
352C23—81no—
353C23—81no—
354C23—81no—
355C23—81no—
356C23#39211yescharacteristic
357C23#44711yescharacteristic
358C23#44911yescharacteristic
359C23#45012yes—
360C23#45111yescharacteristic
361C23#45211yescharacteristic
362C23#45412yes—
363C23#45511yescharacteristic
364C23#45512yes—
365C23#45611yescharacteristic
366C23B(4,𝔽2)12yes—
367Q8—44no—
368Q8—44no—
369Q8—82no—
370Q8—82no—
371Q8—84no—
372Q8—84no—
373D4—44no—
374D4—82no—
375D4—82no—
376D4—82no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—44no—
405C2×C4—42no—
406C2×C4—44no—
407C2×C4—84no—
408C2×C4—82no—
409C2×C4—84no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4#44711yescharacteristic
429C2×C4#44911yescharacteristic
430C2×C4#45111yescharacteristic
431C2×C4#45211yescharacteristic
432C2×C4#46012yes—
433C2×C4#46611yescharacteristic
434C2×C4#46711yescharacteristic
435C2×C4#46911yescharacteristic
436C2×C4#47011yescharacteristic
437C2×C4#49211yescharacteristic
438C2×C4#49611yescharacteristic
439C8—82no—
440C8—82no—
441C8—82no—
442C22—82no—
443C22—84no—
444C22—84no—
445C22—82no—
446C22—82no—
447C22—161no—
448C22—162no—
449C22—162no—
450C22—161no—
451C22—161no—
452C22—161no—
453C22#159712yes—
454C22#159812yes—
455C22#160112yes—
456C22#160212yes—
457C22#160412yes—
458C22#160612yes—
459C22#163512yes—
460C22#163712yes—
461C22#163912yes—
462C22#164111yescharacteristic
463C22#164212yes—
464C22#164411yescharacteristic
465C22#164911yescharacteristic
466C22#165211yescharacteristic
467C22#166212yes—
468C22#166412yes—
469C22#199911yescharacteristic
470C22#200111yescharacteristic
471C22#200311yescharacteristic
472C22#200411yescharacteristic
473C22#200711yescharacteristic
474C22#201411yescharacteristic
475C22#202111yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—22no—
486C4—21no—
487C4—82no—
488C4—84no—
489C4—84no—
490C4—161no—
491C4—161no—
492C2—162no—
493C2#776212yes—
494C2#776412yes—
495C2#777412yes—
496C2#777612yes—
497C2#991511yescharacteristic
498C2#992411yescharacteristic
499C2#996411yescharacteristic
500C2#1006011yescharacteristic
501C2#1006211yescharacteristic
502C2#1008311yescharacteristic
503C2#1023311yescharacteristic
subgroupG/H
center, socleC24#120
commutator, Frattini, cosocleC22×C42C23
prime radicalC23×D4D4
LCSG ▷ C22×C42 ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2043C2semidirect
4. #11384C2semidirect
5. C2×#1271C2semidirect
7. #7025C2semidirect

Maximal subgroups

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

subgroupindex
C2×#20432
C2×#20232
#170712
#113842
C2×#12712
C2×#12702
#70252