Finite Group Databasebeta

← #114395

Subgroups — #114395

Order 512.

908 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3209C211yesmaximal, characteristic
2C2×#1997C211yesmaximal, characteristic
3#21302C211yesmaximal, characteristic
4C2×#1550C211yesmaximal, characteristic
5C22×#333C211yesmaximal, characteristic
6C2×#1301C211yesmaximal, characteristic
7C2×#1283C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C22×C4⋊Q8C2211yescharacteristic
10#3209—22no—
11#3209—22no—
12#3209—22no—
13#3209—22no—
14C2×#494—21no—
15C2×#487—21no—
16C2×#462—22no—
17C2×#451C414yes—
18C2×#431C2211yescharacteristic
19C2×#423C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C2×C4×M16C2211yescharacteristic
23#1997—22no—
24#1997—22no—
25#1985—22no—
26#1984—22no—
27C2×#343—22no—
28#1729—22no—
29#1550—22no—
30#1550—22no—
31C2×#333—22no—
32C2×#333—22no—
33C2×#333—22no—
34C2×#333—21no—
35C2×#332—21no—
36#1301—22no—
37#1283—22no—
38C23×Q8C2×C412yes—
39C22×Q16—24no—
40C22×M16—21no—
41C22×M16D412yes—
42C23×C8—21no—
43C23×C8—21no—
44#533—21no—
45#533—21no—
46#533—21no—
47#533—21no—
48#533—21no—
49#533—21no—
50#533—21no—
51#533—21no—
52C2×C4⋊Q8—21no—
53C2×C4⋊Q8—21no—
54C2×C4⋊Q8—21no—
55C2×C4⋊Q8—21no—
56C2×C4⋊Q8—21no—
57C2×C4⋊Q8—21no—
58C2×C4⋊Q8—21no—
59C2×C4⋊Q8—21no—
60C2×C4⋊Q8—21no—
61C2×C4⋊Q8—21no—
62C2×C4⋊Q8D411yescharacteristic
63C2×C4⋊Q8D412yes—
64C2×C4⋊Q8D412yes—
65C2×C4⋊Q8D411yescharacteristic
66C2×#125—21no—
67C2×C22⋊Q8—21no—
68C2×C22⋊Q8C2×C412yes—
69C2×C4×Q8—21no—
70C2×C4×Q8D412yes—
71C2×#117—21no—
72C22×C4⋊C4—21no—
73C22×C4⋊C4—21no—
74C22×C42C2311yescharacteristic
75#494—24no—
76#494—24no—
77#487—24no—
78#487—24no—
79#462—28no—
80#462—28no—
81#451—28no—
82#451—28no—
83#431—21no—
84#431—21no—
85#431D412yes—
86#431D412yes—
87#423—21no—
88#423—21no—
89#423—21no—
90#423D412yes—
91C2×C4⋊C8—21no—
92C2×C4⋊C8—21no—
93C2×C4⋊C8—21no—
94C2×C4⋊C8—21no—
95C2×C4⋊C8—21no—
96C2×C4⋊C8—21no—
97C2×C4⋊C8—21no—
98C2×C4⋊C8—21no—
99C2×C4⋊C8—21no—
100C2×C4⋊C8—21no—
101C2×C4⋊C8—21no—
102C2×C4⋊C8—21no—
103C2×C4⋊C8—21no—
104C2×C4⋊C8D412yes—
105C2×C4⋊C8D412yes—
106C2×#103—24no—
107C2×C22⋊C8C2×C412yes—
108C4×M16—21no—
109C4×M16—21no—
110C4×M16—21no—
111C4×M16—21no—
112C2×#97—21no—
113C2×C4×C8—21no—
114C2×C4×C8—21no—
115#343—28no—
116#336—28no—
117#333—28no—
118#333—24no—
119#332—24no—
120C22×Q8—22no—
121C22×Q8—21no—
122C22×Q8—22no—
123C22×Q8—22no—
124C22×Q8—22no—
125C22×Q8—22no—
126C22×Q8—84no—
127C22×Q8C22⋊C412yes—
128C22×Q8C22⋊C414yes—
129C23×C4—22no—
130C23×C4C22×C411yescharacteristic
131C23×C4C2×D411yescharacteristic
132C23×C4#4111yescharacteristic
133C2×Q16—216no—
134C2×Q16—88no—
135C2×M16—22no—
136C2×M16—22no—
137C2×M16—22no—
138C2×M16—22no—
139C2×M16—22no—
140C2×M16—22no—
141C2×M16—41no—
142C2×M16—42no—
143C2×M16—42no—
144C2×M16Q1614yescomplemented
145C22×C8—22no—
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—41no—
150C22×C8—41no—
151C22×C8—41no—
152C22×C8—41no—
153C22×C8—41no—
154C22×C8—42no—
155C22×C8—42no—
156C22×C8—82no—
157C4⋊Q8—21no—
158C4⋊Q8—21no—
159C4⋊Q8—21no—
160C4⋊Q8—22no—
161C4⋊Q8—22no—
162C4⋊Q8—22no—
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165C4⋊Q8—21no—
166C4⋊Q8—21no—
167C4⋊Q8—21no—
168C4⋊Q8—22no—
169C4⋊Q8—22no—
170C4⋊Q8—21no—
171C4⋊Q8—22no—
172C4⋊Q8—21no—
173C4⋊Q8—41no—
174C4⋊Q8—41no—
175C4⋊Q8—41no—
176C4⋊Q8—41no—
177C4⋊Q8—41no—
178C4⋊Q8—41no—
179C4⋊Q8—41no—
180C4⋊Q8—41no—
181#125—41no—
182#125—41no—
183#125—41no—
184#125—41no—
185C22⋊Q8—22no—
186C22⋊Q8—22no—
187C22⋊Q8—22no—
188C22⋊Q8—22no—
189C22⋊Q8—41no—
190C22⋊Q8—41no—
191C22⋊Q8—41no—
192C22⋊Q8—41no—
193C4×Q8—22no—
194C4×Q8—22no—
195C4×Q8—22no—
196C4×Q8—22no—
197C4×Q8—41no—
198C4×Q8—41no—
199C4×Q8—41no—
200C4×Q8—41no—
201#117—41no—
202#117—41no—
203#117—41no—
204#117—41no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—41no—
215C2×C4⋊C4—41no—
216C2×C4⋊C4—41no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—41no—
221C2×C4⋊C4—41no—
222C2×C4⋊C4C22⋊C412yes—
223C2×C22⋊C4—22no—
224C2×C42—22no—
225C2×C42C2×D411yescharacteristic
226C2×C42C2×D411yescharacteristic
227C2×C42C2×D411yescharacteristic
228C2×C42C2×D411yescharacteristic
229C2×C42C2×D411yescharacteristic
230C2×C42C2×D411yescharacteristic
231C2×C42C2×D411yescharacteristic
232C2×C42C2×D411yescharacteristic
233C2×C42C2×D411yescharacteristic
234C2×C42#4111yescharacteristic
235C2×C42#4111yescharacteristic
236C2×C42#4111yescharacteristic
237C4⋊C8—22no—
238C4⋊C8—22no—
239C4⋊C8—22no—
240C4⋊C8—22no—
241C4⋊C8—22no—
242C4⋊C8—22no—
243C4⋊C8—22no—
244C4⋊C8—22no—
245C4⋊C8—41no—
246C4⋊C8—41no—
247C4⋊C8—41no—
248C4⋊C8—41no—
249C4⋊C8—41no—
250C4⋊C8—41no—
251#103—216no—
252C22⋊C8—22no—
253C22⋊C8C22⋊C414yes—
254#97—41no—
255#97—41no—
256C4×C8—22no—
257C4×C8—22no—
258C4×C8—41no—
259C4×C8—41no—
260C24C4×D411yescharacteristic
261C2×Q8—24no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—24no—
265C2×Q8—44no—
266C2×Q8—48no—
267C2×Q8—42no—
268C2×Q8—42no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—84no—
274C2×Q8—84no—
275C2×Q8—84no—
276C2×Q8—84no—
277C2×Q8—84no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—84no—
287C22×C4C2×C22⋊C411yescharacteristic
288C22×C4C2×C22⋊C411yescharacteristic
289C22×C4C2×C22⋊C411yescharacteristic
290C22×C4C4×D411yescharacteristic
291C22×C4C4×D411yescharacteristic
292C22×C4C4×D411yescharacteristic
293C22×C4#12011yescharacteristic
294C22×C4#12011yescharacteristic
295C22×C4#12111yescharacteristic
296C22×C4#12111yescharacteristic
297C22×C4#12111yescharacteristic
298C22×C4#12111yescharacteristic
299C22×C4#12111yescharacteristic
300C22×C4#12111yescharacteristic
301C22×C4#12311yescharacteristic
302C22×C4#12311yescharacteristic
303C22×C4#12411yescharacteristic
304C22×C4#12711yescharacteristic
305C22×C4C2×Q1612yes—
306C22×C4#13512yes—
307C22×C4#13712yes—
308C22×C4#13712yes—
309Q16—816no—
310M16—24no—
311M16—24no—
312M16—42no—
313M16—42no—
314M16—44no—
315M16—81no—
316M16—81no—
317C2×C8—24no—
318C2×C8—24no—
319C2×C8—44no—
320C2×C8—42no—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—44no—
326C2×C8—82no—
327C2×C8—82no—
328C2×C8—82no—
329C2×C8—82no—
330C2×C8—81no—
331C2×C8—81no—
332C2×C8—82no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—42no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—41no—
353C22⋊C4—42no—
354C22⋊C4—42no—
355C42—42no—
356C42—42no—
357C42#12011yescharacteristic
358C42#12011yescharacteristic
359C42#12011yescharacteristic
360C42#12011yescharacteristic
361C42#12011yescharacteristic
362C42#12011yescharacteristic
363C42#12111yescharacteristic
364C42#12111yescharacteristic
365C42#12111yescharacteristic
366C42#12111yescharacteristic
367C42#12111yescharacteristic
368C42#12111yescharacteristic
369C42#12311yescharacteristic
370C42#12311yescharacteristic
371C42#12411yescharacteristic
372C42#12711yescharacteristic
373C23—22no—
374C23—22no—
375C23#38611yescharacteristic
376C23#38611yescharacteristic
377C23#39011yescharacteristic
378C23C4×Q1612yes—
379C23#44112yes—
380Q8—44no—
381Q8—48no—
382Q8—82no—
383Q8—84no—
384Q8—84no—
385Q8—84no—
386Q8—82no—
387Q8—81no—
388Q8—81no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—44no—
407C2×C4—84no—
408C2×C4—84no—
409C2×C4—84no—
410C2×C4#37911yescharacteristic
411C2×C4#38611yescharacteristic
412C2×C4#38611yescharacteristic
413C2×C4#39011yescharacteristic
414C2×C4#39211yescharacteristic
415C2×C4#39211yescharacteristic
416C2×C4#39211yescharacteristic
417C2×C4#39211yescharacteristic
418C2×C4#39411yescharacteristic
419C2×C4#39411yescharacteristic
420C2×C4#39411yescharacteristic
421C2×C4#39411yescharacteristic
422C2×C4#45112yes—
423C2×C4#45112yes—
424C2×C4#45212yes—
425C2×C4#45212yes—
426C2×C4#46212yes—
427C2×C4#46212yes—
428C2×C4#46412yes—
429C2×C4#46412yes—
430C2×C4#46712yes—
431C2×C4#47012yes—
432C2×C4#47112yes—
433C2×C4#47312yes—
434C2×C4#49411yescharacteristic
435C2×C4#49511yescharacteristic
436C2×C4#49711yescharacteristic
437C2×C4#49711yescharacteristic
438C8—44no—
439C8—44no—
440C8—82no—
441C8—82no—
442C8—82no—
443C22—21no—
444C22—21no—
445C22—24no—
446C22—24no—
447C22—21no—
448C22—21no—
449C22#143811yescharacteristic
450C22#187812yes—
451C22#187812yes—
452C22#190812yes—
453C22#191412yes—
454C22#196911yescharacteristic
455C22#197111yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—82no—
463C4—82no—
464C4—84no—
465C4#200112yes—
466C4#201511yescharacteristic
467C4#201511yescharacteristic
468C4#201611yescharacteristic
469C4#201611yescharacteristic
470C4#201911yescharacteristic
471C4#202011yescharacteristic
472C4#205212yes—
473C4#205612yes—
474C2—22no—
475C2—21no—
476C2—21no—
477C2#926814yes—
478C2#1097311yescharacteristic
479C2#1102111yescharacteristic
480C2#1102411yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
144. C2×M16Q16semidirect

Maximal subgroups

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

subgroupindex
C2×#32092
C2×#19972
#213022
C2×#15502
C22×#3332
C2×#13012
C2×#12832