Finite Group Databasebeta

← #114393

Subgroups — #114393

Order 512.

876 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×#3230C211yesmaximal, characteristic
2C2×#1997C211yesmaximal, characteristic
3#21302C211yesmaximal, characteristic
4C2×#1550C211yesmaximal, characteristic
5C22×#332C211yesmaximal, characteristic
6C2×#1301C211yesmaximal, characteristic
7C2×#1283C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C22×C4⋊Q8C2211yescharacteristic
10#3230—22no—
11#3230—22no—
12#3230—22no—
13#3230—22no—
14C2×#500—21no—
15C2×#487—21no—
16C2×#484C414yes—
17C2×#477—22no—
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—21no—
32C2×#332—22no—
33C2×#332—22no—
34C2×#332—22no—
35C2×#332—21no—
36#1301—22no—
37#1283—22no—
38C23×Q8—21no—
39C22×M16—21no—
40C22×M16D412yes—
41C23×C8—21no—
42C23×C8—21no—
43#533—21no—
44#533—21no—
45#533—21no—
46#533—21no—
47#533—21no—
48#533—21no—
49#533—21no—
50#533—21no—
51C2×C4⋊Q8—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⋊Q8D411yescharacteristic
62C2×C4⋊Q8D411yescharacteristic
63C2×C4⋊Q8D412yes—
64C2×C4⋊Q8D412yes—
65C2×#125—21no—
66C2×C22⋊Q8—21no—
67C2×C22⋊Q8C2×C412yes—
68C2×C4×Q8—21no—
69C2×C4×Q8D412yes—
70C2×#117—21no—
71C22×C4⋊C4—21no—
72C22×C4⋊C4C2×C412yes—
73C22×C42C2311yescharacteristic
74#500—24no—
75#500—24no—
76#487—24no—
77#487—24no—
78#484—28no—
79#484—28no—
80#477—28no—
81#477—28no—
82#431—21no—
83#431—21no—
84#431D412yes—
85#431D412yes—
86C2×#107—24no—
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—24no—
118#332—28no—
119#332—24no—
120C22×Q8—21no—
121C22×Q8—22no—
122C22×Q8—22no—
123C22×Q8—41no—
124C22×Q8—41no—
125C22×Q8—41no—
126C22×Q8—41no—
127C22×Q8—82no—
128C22×Q8—82no—
129C22×Q8C22⋊C412yes—
130C23×C4—22no—
131C23×C4C22×C411yescharacteristic
132C23×C4C2×D411yescharacteristic
133C23×C4#4111yescharacteristic
134C2×M16—22no—
135C2×M16—22no—
136C2×M16—22no—
137C2×M16—22no—
138C2×M16—22no—
139C2×M16—22no—
140C2×M16—41no—
141C2×M16—42no—
142C2×M16—42no—
143C2×M16Q1614yes—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—41no—
149C22×C8—41no—
150C22×C8—41no—
151C22×C8—41no—
152C22×C8—41no—
153C22×C8—42no—
154C22×C8—42no—
155C22×C8—82no—
156C4⋊Q8—22no—
157C4⋊Q8—22no—
158C4⋊Q8—22no—
159C4⋊Q8—22no—
160C4⋊Q8—22no—
161C4⋊Q8—21no—
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164C4⋊Q8—21no—
165C4⋊Q8—21no—
166C4⋊Q8—21no—
167C4⋊Q8—22no—
168C4⋊Q8—22no—
169C4⋊Q8—22no—
170C4⋊Q8—21no—
171C4⋊Q8—21no—
172C4⋊Q8—41no—
173C4⋊Q8—41no—
174C4⋊Q8—41no—
175C4⋊Q8—41no—
176C4⋊Q8—41no—
177C4⋊Q8—41no—
178C4⋊Q8—41no—
179C4⋊Q8—41no—
180#125—41no—
181#125—41no—
182#125—41no—
183#125—41no—
184C22⋊Q8—22no—
185C22⋊Q8—22no—
186C22⋊Q8—22no—
187C22⋊Q8—22no—
188C22⋊Q8—41no—
189C22⋊Q8—41no—
190C22⋊Q8—41no—
191C22⋊Q8—41no—
192C4×Q8—22no—
193C4×Q8—22no—
194C4×Q8—22no—
195C4×Q8—22no—
196C4×Q8—41no—
197C4×Q8—41no—
198C4×Q8—41no—
199C4×Q8—41no—
200#117—41no—
201#117—41no—
202#117—41no—
203#117—41no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—41no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4C22⋊C414yes—
221C2×C4⋊C4C22⋊C412yes—
222C2×C22⋊C4—22no—
223C2×C42—22no—
224C2×C42C2×D411yescharacteristic
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×C42#4111yescharacteristic
234C2×C42#4111yescharacteristic
235C2×C42#4111yescharacteristic
236#107—216no—
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—22no—
262C2×Q8—22no—
263C2×Q8—44no—
264C2×Q8—41no—
265C2×Q8—42no—
266C2×Q8—41no—
267C2×Q8—42no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—84no—
273C2×Q8—82no—
274C2×Q8—82no—
275C2×Q8—84no—
276C2×Q8—84no—
277C2×Q8—82no—
278C2×Q8—82no—
279C2×Q8—82no—
280C2×Q8—82no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—84no—
290C22×C4C2×C22⋊C411yescharacteristic
291C22×C4C2×C22⋊C411yescharacteristic
292C22×C4C2×C22⋊C411yescharacteristic
293C22×C4C4×D411yescharacteristic
294C22×C4C4×D411yescharacteristic
295C22×C4C4×D411yescharacteristic
296C22×C4#12011yescharacteristic
297C22×C4#12011yescharacteristic
298C22×C4#12111yescharacteristic
299C22×C4#12111yescharacteristic
300C22×C4#12111yescharacteristic
301C22×C4#12111yescharacteristic
302C22×C4#12111yescharacteristic
303C22×C4#12111yescharacteristic
304C22×C4#12311yescharacteristic
305C22×C4#12311yescharacteristic
306C22×C4#12411yescharacteristic
307C22×C4#12711yescharacteristic
308C22×C4C2×Q1612yes—
309C22×C4#13512yes—
310C22×C4#13712yes—
311C22×C4#13712yes—
312M16—24no—
313M16—24no—
314M16—42no—
315M16—42no—
316M16—44no—
317M16—81no—
318M16—81no—
319C2×C8—24no—
320C2×C8—24no—
321C2×C8—44no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—44no—
328C2×C8—82no—
329C2×C8—82no—
330C2×C8—82no—
331C2×C8—82no—
332C2×C8—81no—
333C2×C8—81no—
334C2×C8—82no—
335C4⋊C4—24no—
336C4⋊C4—22no—
337C4⋊C4—24no—
338C4⋊C4—22no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—42no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—41no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C42—42no—
358C42—42no—
359C42#12011yescharacteristic
360C42#12011yescharacteristic
361C42#12011yescharacteristic
362C42#12011yescharacteristic
363C42#12011yescharacteristic
364C42#12011yescharacteristic
365C42#12111yescharacteristic
366C42#12111yescharacteristic
367C42#12111yescharacteristic
368C42#12111yescharacteristic
369C42#12111yescharacteristic
370C42#12111yescharacteristic
371C42#12311yescharacteristic
372C42#12311yescharacteristic
373C42#12411yescharacteristic
374C42#12711yescharacteristic
375C23—22no—
376C23—22no—
377C23#38611yescharacteristic
378C23#38611yescharacteristic
379C23#39011yescharacteristic
380C23C4×Q1612yes—
381C23#44112yes—
382Q8—44no—
383Q8—82no—
384Q8—84no—
385Q8—84no—
386Q8—82no—
387Q8—84no—
388Q8—81no—
389Q8—82no—
390Q8—81no—
391Q8—82no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—44no—
410C2×C4—84no—
411C2×C4—84no—
412C2×C4—84no—
413C2×C4#37911yescharacteristic
414C2×C4#38611yescharacteristic
415C2×C4#38611yescharacteristic
416C2×C4#39011yescharacteristic
417C2×C4#39211yescharacteristic
418C2×C4#39211yescharacteristic
419C2×C4#39211yescharacteristic
420C2×C4#39211yescharacteristic
421C2×C4#39411yescharacteristic
422C2×C4#39411yescharacteristic
423C2×C4#39411yescharacteristic
424C2×C4#39411yescharacteristic
425C2×C4#45112yes—
426C2×C4#45112yes—
427C2×C4#45212yes—
428C2×C4#45212yes—
429C2×C4#46212yes—
430C2×C4#46212yes—
431C2×C4#46412yes—
432C2×C4#46412yes—
433C2×C4#46712yes—
434C2×C4#47012yes—
435C2×C4#47112yes—
436C2×C4#47212yes—
437C2×C4#49411yescharacteristic
438C2×C4#49511yescharacteristic
439C2×C4#49711yescharacteristic
440C2×C4#49711yescharacteristic
441C8—44no—
442C8—44no—
443C8—82no—
444C8—82no—
445C8—82no—
446C22—21no—
447C22—21no—
448C22—24no—
449C22—24no—
450C22—21no—
451C22—21no—
452C22#143811yescharacteristic
453C22#187812yes—
454C22#187812yes—
455C22#190712yes—
456C22#191512yes—
457C22#196911yescharacteristic
458C22#197111yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—82no—
466C4—84no—
467C4—82no—
468C4#200112yes—
469C4#201511yescharacteristic
470C4#201511yescharacteristic
471C4#201611yescharacteristic
472C4#201611yescharacteristic
473C4#201811yescharacteristic
474C4#201911yescharacteristic
475C4#205112yes—
476C4#205612yes—
477C2—22no—
478C2—21no—
479C2—21no—
480C2#927014yes—
481C2#1097411yescharacteristic
482C2#1102011yescharacteristic
483C2#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

Maximal subgroups

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

subgroupindex
C2×#32302
C2×#19972
#213022
C2×#15502
C22×#3322
C2×#13012
C2×#12832