Finite Group Databasebeta

← #148693

Subgroups — #148693

Order 512.

738 conjugacy classes of subgroups.

The subgroup lattice has 485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1801C211yesmaximal, characteristic
2#13978C211yesmaximal, characteristic
3C2×#1394C212yesmaximal
4C2×#1394C212yesmaximal
5#10763C211yesmaximal, characteristic
6C22×C4×Q8C2211yescharacteristic
7C2×#423—21no—
8C22×#101C2212yes—
9C22×#101C2212yes—
10C2×#391C2211yescharacteristic
11C2×#391C2211yescharacteristic
12C2×#389C411yescharacteristic
13C2×#382C411yescharacteristic
14#1801—24no—
15C2×#343—21no—
16C2×#343—21no—
17#1728—21no—
18#1442—21no—
19#1442—21no—
20#1436—21no—
21#1436—21no—
22C4⋊#95C411yescharacteristic
23C4×#95C411yescharacteristic
24#1394—24no—
25#1394—24no—
26C23×Q8C2311yescharacteristic
27C22×M16—22no—
28C22×M16—22no—
29C2×C4×Q8—22no—
30C2×C4×Q8—22no—
31C2×C4×Q8—41no—
32C2×C4×Q8—41no—
33C2×C4×Q8—42no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4C2×C411yescharacteristic
36C22×C4⋊C4C2×C411yescharacteristic
37C22×C4⋊C4C2×C411yescharacteristic
38C22×C4⋊C4D411yescharacteristic
39C22×C4⋊C4D411yescharacteristic
40C22×C42C2×C411yescharacteristic
41C22×C42C2×C411yescharacteristic
42C22×C42C2×C411yescharacteristic
43C22×C42D411yescharacteristic
44C22×C42D411yescharacteristic
45#423—24no—
46#423—42no—
47C2×C4⋊C8—41no—
48C2×C4⋊C8—41no—
49C2×#101—22no—
50C2×#101—22no—
51C2×#101—22no—
52C2×#101—22no—
53C2×#101—22no—
54C2×#101—22no—
55C2×#101—22no—
56C2×#101—22no—
57C2×#101—22no—
58C2×#101—22no—
59C2×#101D414yes—
60C2×#101Q814yes—
61#391—21no—
62#391—21no—
63#391—22no—
64#391—22no—
65#391D412yes—
66#391Q812yes—
67#389—41no—
68#389—41no—
69#382—42no—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—21no—
73C2×#95—21no—
74C2×#95—21no—
75C2×#95—21no—
76C2×#95—21no—
77C2×#95—21no—
78C2×#95—21no—
79C2×#95—21no—
80C2×#95—21no—
81#343—24no—
82#343—42no—
83#336—41no—
84#336—41no—
85C22×Q8—41no—
86C22×Q8—41no—
87C22×Q8—41no—
88C22×Q8—41no—
89C22×Q8C2×D411yescharacteristic
90C22×Q8C2×D412yes—
91C22×Q8C2×Q811yescharacteristic
92C22×Q8C2×Q812yes—
93C22×Q8#4111yescharacteristic
94C22×Q8#4111yescharacteristic
95C22×Q8#4112yes—
96C22×Q8#4112yes—
97C23×C4—21no—
98C23×C4—21no—
99C23×C4—21no—
100C23×C4—21no—
101C23×C4C22⋊C411yescharacteristic
102C23×C4C22⋊C411yescharacteristic
103C23×C4C22⋊C411yescharacteristic
104C23×C4C22⋊C411yescharacteristic
105C23×C4C22×C411yescharacteristic
106C23×C4C2×D411yescharacteristic
107C23×C4C2×D411yescharacteristic
108C2×M16—24no—
109C2×M16—24no—
110C2×M16—42no—
111C2×M16—42no—
112C2×M16—42no—
113C2×M16—42no—
114C2×M16—42no—
115C2×M16—42no—
116C2×M16—42no—
117C2×M16—42no—
118C2×M16—42no—
119C2×M16—42no—
120C22×C8—42no—
121C22×C8—42no—
122C4×Q8—44no—
123C4×Q8—44no—
124C4×Q8—44no—
125C4×Q8—44no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—42no—
143C2×C4⋊C4—42no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4C4⋊C412yes—
147C2×C42—21no—
148C2×C42—21no—
149C2×C42—22no—
150C2×C42—21no—
151C2×C42—21no—
152C2×C42—21no—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—21no—
156C2×C42—21no—
157C2×C42—22no—
158C2×C42—22no—
159C2×C42—22no—
160C2×C42—41no—
161C2×C42—41no—
162C2×C42—41no—
163C2×C42—41no—
164C2×C42—41no—
165C2×C42—41no—
166C2×C42C4⋊C412yes—
167C4⋊C8—44no—
168C4⋊C8—44no—
169#101—24no—
170#101—24no—
171#101—24no—
172#101—24no—
173#101—42no—
174#101—42no—
175#101—42no—
176#101—42no—
177#95—22no—
178#95—22no—
179#95—22no—
180#95—22no—
181#95—42no—
182#95—42no—
183#95—42no—
184#95—42no—
185#95—42no—
186#95—42no—
187#95—42no—
188#95—41no—
189#95—42no—
190#95—41no—
191C24C2×C22⋊C411yescharacteristic
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8—42no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8—42no—
200C2×Q8—42no—
201C2×Q8—41no—
202C2×Q8—41no—
203C2×Q8—41no—
204C2×Q8—41no—
205C2×Q8—42no—
206C2×Q8—42no—
207C2×Q8—42no—
208C2×Q8#12112yes—
209C2×Q8C22⋊Q812yes—
210C2×Q8C22⋊Q812yes—
211C2×Q8#12312yes—
212C2×Q8#12512yes—
213C2×Q8#12512yes—
214C2×Q8#12612yes—
215C2×Q8C4⋊Q812yes—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
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×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4#9911yescharacteristic
275C22×C4#9911yescharacteristic
276C22×C4#9912yes—
277C22×C4C2×C4⋊C411yescharacteristic
278C22×C4#11711yescharacteristic
279C22×C4C4×D412yes—
280C22×C4C4×Q812yes—
281C22×C4#12011yescharacteristic
282C22×C4#12111yescharacteristic
283C22×C4#12111yescharacteristic
284C22×C4#12112yes—
285C22×C4C22⋊Q811yescharacteristic
286C22×C4C22⋊Q812yes—
287C22×C4C22⋊Q811yescharacteristic
288C22×C4#12311yescharacteristic
289C22×C4#12411yescharacteristic
290C22×C4C4⋊Q811yescharacteristic
291M16—44no—
292M16—44no—
293M16—44no—
294M16—44no—
295M16—82no—
296M16—82no—
297M16—82no—
298M16—82no—
299C2×C8—44no—
300C2×C8—44no—
301C2×C8—82no—
302C2×C8—82no—
303C2×C8—82no—
304C2×C8—82no—
305C4⋊C4—44no—
306C4⋊C4—44no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—82no—
312C4⋊C4—82no—
313C4⋊C4—82no—
314C42—22no—
315C42—22no—
316C42—22no—
317C42—22no—
318C42—42no—
319C42—42no—
320C42—42no—
321C42—42no—
322C42—42no—
323C42—42no—
324C42—82no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23#38011yescharacteristic
330C23#38611yescharacteristic
331C23#39111yescharacteristic
332C23C2×#9911yescharacteristic
333C23C2×#9911yescharacteristic
334C23#41011yescharacteristic
335C23#41011yescharacteristic
336Q8—42no—
337Q8—42no—
338Q8—42no—
339Q8—42no—
340Q8—42no—
341Q8—42no—
342Q8—42no—
343Q8—42no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4#35512yes—
423C2×C4#38712yes—
424C2×C4#38912yes—
425C2×C4#39411yescharacteristic
426C2×C4#39511yescharacteristic
427C2×C4#39612yes—
428C2×C4#39812yes—
429C2×C4#39811yescharacteristic
430C2×C4#40011yescharacteristic
431C8—84no—
432C8—84no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22#144111yescharacteristic
446C22#179911yescharacteristic
447C22#179911yescharacteristic
448C22#189811yescharacteristic
449C22#189911yescharacteristic
450C22#199611yescharacteristic
451C22#199611yescharacteristic
452C22C2×#35511yescharacteristic
453C22#213211yescharacteristic
454C22#213311yescharacteristic
455C22#213511yescharacteristic
456C4—22no—
457C4—21no—
458C4—22no—
459C4—22no—
460C4—22no—
461C4—21no—
462C4—21no—
463C4—22no—
464C4—21no—
465C4—41no—
466C4—42no—
467C4—82no—
468C4—82no—
469C4—82no—
470C4—81no—
471C4—81no—
472C4—161no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2—21no—
477C2#1120311yescharacteristic
478C2#1280111yescharacteristic
479C2#1280411yescharacteristic
480C2#1309211yescharacteristic
481C2#1309511yescharacteristic
482C2#1330111yescharacteristic
483C2#1330311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC23×C4C22×C4
Frattini, cosocleC23×Q8C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C23×Q8 ▷ C22 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#18012
#139782
C2×#13942
#107632