Finite Group Databasebeta

← #72277787

Subgroups — #72277787

Order 8064.

2644 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 2644 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72277753C312yesmaximal, complemented
2#72277737C311yesmaximal, characteristic, complemented
3#72276787C211yesmaximal, characteristic, complemented
4C2×#72214606C211yesmaximal, characteristic, complemented
5#72276534C311yesmaximal, characteristic, complemented
6A4×(C22⋊D7)⋊C3—41nomaximal
7C22×ΓL(1,𝔽8)×C22⋊A4C211yesmaximal, characteristic, complemented
8C2×ΓL(1,𝔽8)×C22⋊A4—21no—
9C2×ΓL(1,𝔽8)×C22⋊A4C2211yescharacteristic
10#72214606—21no—
11C22×C22⋊(C22⋊ΓL(1,𝔽8))C2×C312yescomplemented
12C22×C7×C22⋊A4C2×C311yescharacteristic, complemented
13C26×ΓL(1,𝔽8)C2×C311yescharacteristic, complemented
14C2×#10620804C2×C312yescomplemented
15C2×#10620796C2×C311yescharacteristic, complemented
16C2×#10620789—31no—
17C2×#10620789—31no—
18C2×#10620789C2×C311yescharacteristic, complemented
19#13052184C2×C312yescomplemented
20#13052164C2×C311yescharacteristic, complemented
21#13052147—31no—
22#13052147—31no—
23#13052147C2×C311yescharacteristic, complemented
24C3×AΣL(1,𝔽64)—71nomaximal, Hall
25ΓL(1,𝔽8)×C22⋊A4D411yescharacteristic, complemented
26C22×A4×ΓL(1,𝔽8)—41no—
27C22×A4×ΓL(1,𝔽8)—82no—
28C2×A4×AGL(1,𝔽7)—41no—
29A4×ΓL(1,𝔽8)⋊C4—41no—
30#11741573C3211yescharacteristic, complemented, Hall
31C2×C22⋊(C22⋊ΓL(1,𝔽8))—22no—
32C2×C22⋊(C22⋊ΓL(1,𝔽8))C22×C312yes—
33C2×C7×C22⋊A4—21no—
34C2×C7×C22⋊A4C22×C311yescharacteristic
35C25×ΓL(1,𝔽8)—21no—
36C25×ΓL(1,𝔽8)—31no—
37C25×ΓL(1,𝔽8)—31no—
38C25×ΓL(1,𝔽8)—62no—
39C25×ΓL(1,𝔽8)—62no—
40C25×ΓL(1,𝔽8)—64no—
41C25×ΓL(1,𝔽8)—61no—
42C25×ΓL(1,𝔽8)C22×C311yescharacteristic
43(C22⋊D7)⋊A4—42no—
44A4×C22⋊D7—41no—
45C22×(C22⋊D7)⋊C3—31no—
46C22×(C22⋊D7)⋊C3—31no—
47C22×(C22⋊D7)⋊C3A411yescharacteristic, complemented
48#10620804—22no—
49#10620796—21no—
50#10620789—21no—
51#10620789—62no—
52#10620789—64no—
53#10620789—62no—
54#10620789—61no—
55C2×(C22⋊Dic7)⋊C3—32no—
56C2×(C22⋊Dic7)⋊C3—31no—
57C2×(C22⋊Dic7)⋊C3—31no—
58C2×(C22⋊Dic7)⋊C3—31no—
59C2×(C22⋊Dic7)⋊C3—31no—
60C2×(C22⋊Dic7)⋊C3—31no—
61C22×C3×C22⋊A4—71no—
62C2×C3×#120⋊C3—71no—
63C3×#379⋊C3—71no—
64C2×A4×ΓL(1,𝔽8)—41no—
65C2×A4×ΓL(1,𝔽8)—81no—
66C2×A4×ΓL(1,𝔽8)—82no—
67C2×A4×ΓL(1,𝔽8)—84no—
68A4×AGL(1,𝔽7)—81no—
69C3×(C22⋊D7)⋊C3—161no—
70C26×C7C2×C3211yescharacteristic, complemented
71C2×#6516—31no—
72C2×#6516—31no—
73C2×#6516C2×C3211yescharacteristic, complemented
74#90019—31no—
75#90019—31no—
76#90019C2×C3211yescharacteristic, complemented
77C3×#2846—71no—
78AΣL(1,𝔽64)—72no—
79AΣL(1,𝔽64)—71no—
80C22⋊(C22⋊ΓL(1,𝔽8))C3×D412yescomplemented
81C7×C22⋊A4C3×D411yescharacteristic, complemented
82C22×C22⋊ΓL(1,𝔽8)—42no—
83C22×C22⋊ΓL(1,𝔽8)—84no—
84C22×C7×A4—41no—
85C22×C7×A4—82no—
86C24×ΓL(1,𝔽8)—22no—
87C24×ΓL(1,𝔽8)—31no—
88C24×ΓL(1,𝔽8)—31no—
89C24×ΓL(1,𝔽8)—34no—
90C24×ΓL(1,𝔽8)—32no—
91C24×ΓL(1,𝔽8)—32no—
92C24×ΓL(1,𝔽8)—31no—
93C24×ΓL(1,𝔽8)—61no—
94C24×ΓL(1,𝔽8)—61no—
95C24×ΓL(1,𝔽8)—62no—
96C24×ΓL(1,𝔽8)—64no—
97C24×ΓL(1,𝔽8)—64no—
98C24×ΓL(1,𝔽8)—62no—
99C24×ΓL(1,𝔽8)—64no—
100C24×ΓL(1,𝔽8)—62no—
101C24×ΓL(1,𝔽8)—62no—
102C24×ΓL(1,𝔽8)—64no—
103C24×ΓL(1,𝔽8)—64no—
104C24×ΓL(1,𝔽8)—62no—
105C24×ΓL(1,𝔽8)—62no—
106C24×ΓL(1,𝔽8)—61no—
107C24×ΓL(1,𝔽8)—61no—
108C24×ΓL(1,𝔽8)—62no—
109C24×ΓL(1,𝔽8)—64no—
110C24×ΓL(1,𝔽8)—64no—
111C24×ΓL(1,𝔽8)—64no—
112C24×ΓL(1,𝔽8)—64no—
113C24×ΓL(1,𝔽8)—68no—
114C24×ΓL(1,𝔽8)—68no—
115C24×ΓL(1,𝔽8)—68no—
116C24×ΓL(1,𝔽8)—64no—
117C24×ΓL(1,𝔽8)—68no—
118C24×ΓL(1,𝔽8)—64no—
119C24×ΓL(1,𝔽8)—62no—
120C24×ΓL(1,𝔽8)—64no—
121C24×ΓL(1,𝔽8)—62no—
122C24×ΓL(1,𝔽8)C3×D411yescharacteristic, complemented
123C24×ΓL(1,𝔽8)C2×A411yescharacteristic
124C2×D7⋊A4—42no—
125C2×A4×D7—41no—
126C23×AGL(1,𝔽7)C2×A411yescharacteristic, complemented
127Dic7⋊A4—42no—
128A4×Dic7—41no—
129C2×(C22⋊D7)⋊C3—61no—
130C2×(C22⋊D7)⋊C3—61no—
131C2×(C22⋊D7)⋊C3—61no—
132C2×(C22⋊D7)⋊C3—62no—
133C2×(C22⋊D7)⋊C3—62no—
134C2×(C22⋊D7)⋊C3—64no—
135C2×(C22⋊D7)⋊C3—62no—
136C2×(C22⋊D7)⋊C3—61no—
137C22×ΓL(1,𝔽8)⋊C4—31no—
138C22×ΓL(1,𝔽8)⋊C4—31no—
139C22×ΓL(1,𝔽8)⋊C4C2×A411yescharacteristic, complemented
140(C22⋊Dic7)⋊C3—62no—
141(C22⋊Dic7)⋊C3—62no—
142(C22⋊Dic7)⋊C3—64no—
143(C22⋊Dic7)⋊C3—62no—
144(C22⋊Dic7)⋊C3—61no—
145(C22⋊Dic7)⋊C3—61no—
146(C22⋊Dic7)⋊C3—61no—
147(C22⋊Dic7)⋊C3—61no—
148C2×C3×C22⋊A4—71no—
149C2×C3×C22⋊A4—141no—
150C3×D4×A4—281no—
151C3×#120⋊C3—141no—
152C22×C3×ΓL(1,𝔽8)—161no—
153C2×C3×AGL(1,𝔽7)—161no—
154A4×ΓL(1,𝔽8)—41no—
155A4×ΓL(1,𝔽8)—82no—
156C3×ΓL(1,𝔽8)⋊C4—161no—
157C25×C7—21no—
158C25×C7—31no—
159C25×C7—31no—
160C25×C7—62no—
161C25×C7—62no—
162C25×C7—64no—
163C25×C7—61no—
164C25×C7C22×C3211yescharacteristic
165C22×C22⋊D7—31no—
166C22×C22⋊D7—31no—
167C22×C22⋊D7C3×A411yescharacteristic, complemented
168#6516—21no—
169#6516—62no—
170#6516—64no—
171#6516—62no—
172#6516—61no—
173C2×C22⋊Dic7—32no—
174C2×C22⋊Dic7—31no—
175C2×C22⋊Dic7—31no—
176C2×C22⋊Dic7—31no—
177C2×C22⋊Dic7—31no—
178C2×C22⋊Dic7—31no—
179C26×C3—71no—
180C22×C22⋊A4—72no—
181C22×C22⋊A4AGL(1,𝔽7)11yescharacteristic, complemented
182C2×C3×#120—71no—
183C2×C3×#120—211no—
184C2×C3×#120—211no—
185C2×#120⋊C3—72no—
186C2×#120⋊C3—71no—
187C3×#379—71no—
188C3×#379—211no—
189C3×#379—211no—
190#379⋊C3—72no—
191#379⋊C3—71no—
192C2×C22⋊ΓL(1,𝔽8)—42no—
193C2×C22⋊ΓL(1,𝔽8)—84no—
194C2×C22⋊ΓL(1,𝔽8)—82no—
195C2×C22⋊ΓL(1,𝔽8)—88no—
196C2×C7×A4—41no—
197C2×C7×A4—82no—
198C2×C7×A4—81no—
199C2×C7×A4—84no—
200C23×ΓL(1,𝔽8)—24no—
201C23×ΓL(1,𝔽8)—22no—
202C23×ΓL(1,𝔽8)—21no—
203C23×ΓL(1,𝔽8)—34no—
204C23×ΓL(1,𝔽8)—32no—
205C23×ΓL(1,𝔽8)—32no—
206C23×ΓL(1,𝔽8)—32no—
207C23×ΓL(1,𝔽8)—31no—
208C23×ΓL(1,𝔽8)—31no—
209C23×ΓL(1,𝔽8)—31no—
210C23×ΓL(1,𝔽8)—31no—
211C23×ΓL(1,𝔽8)—62no—
212C23×ΓL(1,𝔽8)—62no—
213C23×ΓL(1,𝔽8)—64no—
214C23×ΓL(1,𝔽8)—61no—
215C23×ΓL(1,𝔽8)—61no—
216C23×ΓL(1,𝔽8)—62no—
217C23×ΓL(1,𝔽8)—62no—
218C23×ΓL(1,𝔽8)—62no—
219C23×ΓL(1,𝔽8)—62no—
220C23×ΓL(1,𝔽8)—62no—
221C23×ΓL(1,𝔽8)—64no—
222C23×ΓL(1,𝔽8)—62no—
223C23×ΓL(1,𝔽8)—62no—
224C23×ΓL(1,𝔽8)—64no—
225C23×ΓL(1,𝔽8)—68no—
226C23×ΓL(1,𝔽8)—62no—
227C23×ΓL(1,𝔽8)—64no—
228C23×ΓL(1,𝔽8)—64no—
229C23×ΓL(1,𝔽8)—64no—
230C23×ΓL(1,𝔽8)—68no—
231C23×ΓL(1,𝔽8)—62no—
232C23×ΓL(1,𝔽8)—64no—
233C23×ΓL(1,𝔽8)—64no—
234C23×ΓL(1,𝔽8)—62no—
235C23×ΓL(1,𝔽8)—62no—
236C23×ΓL(1,𝔽8)—64no—
237C23×ΓL(1,𝔽8)—62no—
238C23×ΓL(1,𝔽8)—62no—
239C23×ΓL(1,𝔽8)—64no—
240C23×ΓL(1,𝔽8)—64no—
241C23×ΓL(1,𝔽8)—68no—
242C23×ΓL(1,𝔽8)—64no—
243C23×ΓL(1,𝔽8)—64no—
244C23×ΓL(1,𝔽8)—68no—
245C23×ΓL(1,𝔽8)—64no—
246C23×ΓL(1,𝔽8)—64no—
247C23×ΓL(1,𝔽8)—68no—
248C23×ΓL(1,𝔽8)—64no—
249C23×ΓL(1,𝔽8)—68no—
250C23×ΓL(1,𝔽8)—64no—
251C23×ΓL(1,𝔽8)—64no—
252C23×ΓL(1,𝔽8)—68no—
253C23×ΓL(1,𝔽8)—64no—
254C23×ΓL(1,𝔽8)—68no—
255C23×ΓL(1,𝔽8)—68no—
256C23×ΓL(1,𝔽8)—64no—
257C23×ΓL(1,𝔽8)—68no—
258C23×ΓL(1,𝔽8)—68no—
259C23×ΓL(1,𝔽8)—68no—
260C23×ΓL(1,𝔽8)—68no—
261C23×ΓL(1,𝔽8)—64no—
262C23×ΓL(1,𝔽8)—62no—
263C23×ΓL(1,𝔽8)—61no—
264C23×ΓL(1,𝔽8)C22×A411yescharacteristic
265D7⋊A4—82no—
266A4×D7—81no—
267C22×AGL(1,𝔽7)—21no—
268C22×AGL(1,𝔽7)—61no—
269C22×AGL(1,𝔽7)—61no—
270C3×C22⋊D7—161no—
271(C22⋊D7)⋊C3—41no—
272(C22⋊D7)⋊C3—121no—
273(C22⋊D7)⋊C3—122no—
274(C22⋊D7)⋊C3—122no—
275(C22⋊D7)⋊C3—124no—
276(C22⋊D7)⋊C3—162no—
277C2×ΓL(1,𝔽8)⋊C4—61no—
278C2×ΓL(1,𝔽8)⋊C4—62no—
279C2×ΓL(1,𝔽8)⋊C4—61no—
280C2×ΓL(1,𝔽8)⋊C4—61no—
281C2×ΓL(1,𝔽8)⋊C4—61no—
282C2×ΓL(1,𝔽8)⋊C4—61no—
283C3×C22⋊A4—71no—
284C22×C3×A4—281no—
285C22×C3×A4—281no—
286C22×C3×A4—562no—
287C3×C4×A4—281no—
288#2846—71noSylow
289C2×C3×ΓL(1,𝔽8)—161no—
290C2×C3×ΓL(1,𝔽8)—321no—
291C3×AGL(1,𝔽7)—321no—
292C24×C7—22no—
293C24×C7—31no—
294C24×C7—31no—
295C24×C7—34no—
296C24×C7—32no—
297C24×C7—32no—
298C24×C7—31no—
299C24×C7—61no—
300C24×C7—61no—
301C24×C7—62no—
302C24×C7—64no—
303C24×C7—64no—
304C24×C7—62no—
305C24×C7—62no—
306C24×C7—64no—
307C24×C7—62no—
308C24×C7—64no—
309C24×C7—64no—
310C24×C7—62no—
311C24×C7—62no—
312C24×C7—61no—
313C24×C7—61no—
314C24×C7—62no—
315C24×C7—64no—
316C24×C7—64no—
317C24×C7—64no—
318C24×C7—64no—
319C24×C7—68no—
320C24×C7—68no—
321C24×C7—68no—
322C24×C7—64no—
323C24×C7—68no—
324C24×C7—64no—
325C24×C7—62no—
326C24×C7—64no—
327C24×C7—62no—
328C24×C7C32×D411yescharacteristic, complemented
329C24×C7C2×C3×A411yescharacteristic
330C23×D7C2×C3×A411yescharacteristic, complemented
331C2×C22⋊D7—61no—
332C2×C22⋊D7—61no—
333C2×C22⋊D7—61no—
334C2×C22⋊D7—62no—
335C2×C22⋊D7—62no—
336C2×C22⋊D7—64no—
337C2×C22⋊D7—62no—
338C2×C22⋊D7—61no—
339C22×Dic7—31no—
340C22×Dic7—31no—
341C22×Dic7C2×C3×A411yescharacteristic, complemented
342C22⋊Dic7—62no—
343C22⋊Dic7—62no—
344C22⋊Dic7—64no—
345C22⋊Dic7—62no—
346C22⋊Dic7—61no—
347C22⋊Dic7—61no—
348C22⋊Dic7—61no—
349C22⋊Dic7—61no—
350C25×C3—71no—
351C25×C3—141no—
352C25×C3—211no—
353C25×C3—211no—
354C25×C3—422no—
355C25×C3—422no—
356C25×C3—424no—
357C25×C3—421no—
358C2×C22⋊A4—21no—
359C2×C22⋊A4—72no—
360C2×C22⋊A4—142no—
361C2×C22⋊A4C2×AGL(1,𝔽7)11yescharacteristic
362C22×C3×D4—71no—
363C22×C3×D4—211no—
364C22×C3×D4—211no—
365D4×A4—281no—
366D4×A4—282no—
367C3×#120—141no—
368C3×#120—422no—
369C3×#120—424no—
370C3×#120—422no—
371C3×#120—421no—
372C2×C3×C22⋊C4—211no—
373C2×C3×C22⋊C4—211no—
374C2×C3×C22⋊C4—211no—
375C2×C3×C22⋊C4—212no—
376C2×C3×C22⋊C4—211no—
377C2×C3×C22⋊C4—211no—
378#120⋊C3—142no—
379#120⋊C3—141no—
380C22×C3×C7—161no—
381C2×C3×D7—161no—
382C22⋊ΓL(1,𝔽8)—42no—
383C22⋊ΓL(1,𝔽8)—84no—
384C7×A4—41no—
385C7×A4—82no—
386C22×ΓL(1,𝔽8)—22no—
387C22×ΓL(1,𝔽8)—31no—
388C22×ΓL(1,𝔽8)—31no—
389C22×ΓL(1,𝔽8)—34no—
390C22×ΓL(1,𝔽8)—32no—
391C22×ΓL(1,𝔽8)—32no—
392C22×ΓL(1,𝔽8)—31no—
393C22×ΓL(1,𝔽8)—61no—
394C22×ΓL(1,𝔽8)—61no—
395C22×ΓL(1,𝔽8)—64no—
396C22×ΓL(1,𝔽8)—64no—
397C22×ΓL(1,𝔽8)—61no—
398C22×ΓL(1,𝔽8)—61no—
399C22×ΓL(1,𝔽8)—64no—
400C22×ΓL(1,𝔽8)—62no—
401C22×ΓL(1,𝔽8)—64no—
402C22×ΓL(1,𝔽8)—62no—
403C22×ΓL(1,𝔽8)—64no—
404C22×ΓL(1,𝔽8)—62no—
405C22×ΓL(1,𝔽8)—62no—
406C22×ΓL(1,𝔽8)—64no—
407C22×ΓL(1,𝔽8)—62no—
408C22×ΓL(1,𝔽8)—62no—
409C22×ΓL(1,𝔽8)—62no—
410C22×ΓL(1,𝔽8)—64no—
411C22×ΓL(1,𝔽8)—64no—
412C22×ΓL(1,𝔽8)—64no—
413C22×ΓL(1,𝔽8)—64no—
414C22×ΓL(1,𝔽8)—68no—
415C22×ΓL(1,𝔽8)—68no—
416C22×ΓL(1,𝔽8)—64no—
417C22×ΓL(1,𝔽8)—68no—
418C22×ΓL(1,𝔽8)—68no—
419C22×ΓL(1,𝔽8)—64no—
420C22×ΓL(1,𝔽8)—62no—
421C22×ΓL(1,𝔽8)—62no—
422C22×ΓL(1,𝔽8)—162no—
423C22×ΓL(1,𝔽8)#120⋊C311yescharacteristic, complemented
424C22×ΓL(1,𝔽8)D4×A411yescharacteristic
425C2×AGL(1,𝔽7)—41no—
426C2×AGL(1,𝔽7)—121no—
427C2×AGL(1,𝔽7)—121no—
428C2×AGL(1,𝔽7)—162no—
429C3×Dic7—161no—
430ΓL(1,𝔽8)⋊C4—41no—
431ΓL(1,𝔽8)⋊C4—121no—
432ΓL(1,𝔽8)⋊C4—121no—
433ΓL(1,𝔽8)⋊C4—162no—
434C2×C3×A4—281no—
435C2×C3×A4—562no—
436C2×C3×A4—561no—
437C2×C3×A4—564no—
438C2×C3×A4—561no—
439C32×D4—1121no—
440C26C3×AGL(1,𝔽7)11yescharacteristic, complemented
441C2×#120—71no—
442C2×#120—211no—
443C2×#120—211no—
444#379—71no—
445#379—211no—
446#379—211no—
447C3×ΓL(1,𝔽8)—161noHall
448C23×C7—24no—
449C23×C7—22no—
450C23×C7—21no—
451C23×C7—32no—
452C23×C7—34no—
453C23×C7—32no—
454C23×C7—32no—
455C23×C7—31no—
456C23×C7—31no—
457C23×C7—31no—
458C23×C7—31no—
459C23×C7—62no—
460C23×C7—62no—
461C23×C7—64no—
462C23×C7—61no—
463C23×C7—62no—
464C23×C7—61no—
465C23×C7—62no—
466C23×C7—62no—
467C23×C7—62no—
468C23×C7—62no—
469C23×C7—64no—
470C23×C7—62no—
471C23×C7—62no—
472C23×C7—64no—
473C23×C7—68no—
474C23×C7—62no—
475C23×C7—64no—
476C23×C7—64no—
477C23×C7—64no—
478C23×C7—68no—
479C23×C7—62no—
480C23×C7—64no—
481C23×C7—64no—
482C23×C7—62no—
483C23×C7—62no—
484C23×C7—64no—
485C23×C7—62no—
486C23×C7—62no—
487C23×C7—64no—
488C23×C7—64no—
489C23×C7—68no—
490C23×C7—64no—
491C23×C7—64no—
492C23×C7—68no—
493C23×C7—64no—
494C23×C7—64no—
495C23×C7—68no—
496C23×C7—64no—
497C23×C7—68no—
498C23×C7—64no—
499C23×C7—64no—
500C23×C7—68no—
501C23×C7—64no—
502C23×C7—68no—
503C23×C7—68no—
504C23×C7—64no—
505C23×C7—68no—
506C23×C7—68no—
507C23×C7—68no—
508C23×C7—68no—
509C23×C7—64no—
510C23×C7—61no—
511C23×C7—62no—
512C23×C7C22×C3×A411yescharacteristic
513C22×D7—21no—
514C22×D7—61no—
515C22×D7—61no—
516C22⋊D7—41no—
517C22⋊D7—121no—
518C22⋊D7—122no—
519C22⋊D7—122no—
520C22⋊D7—124no—
521C2×Dic7—61no—
522C2×Dic7—61no—
523C2×Dic7—62no—
524C2×Dic7—61no—
525C2×Dic7—61no—
526C2×Dic7—61no—
527C24×C3—71no—
528C24×C3—71no—
529C24×C3—71no—
530C24×C3—142no—
531C24×C3—211no—
532C24×C3—211no—
533C24×C3—212no—
534C24×C3—214no—
535C24×C3—212no—
536C24×C3—211no—
537C24×C3—422no—
538C24×C3—421no—
539C24×C3—421no—
540C24×C3—424no—
541C24×C3—422no—
542C24×C3—424no—
543C24×C3—422no—
544C24×C3—421no—
545C24×C3—421no—
546C24×C3—422no—
547C24×C3—422no—
548C24×C3—424no—
549C24×C3—422no—
550C24×C3—424no—
551C24×C3—424no—
552C24×C3—422no—
553C24×C3—424no—
554C24×C3—422no—
555C24×C3—422no—
556C24×C3—424no—
557C24×C3—424no—
558C24×C3—424no—
559C24×C3—424no—
560C24×C3—424no—
561C24×C3—428no—
562C24×C3—428no—
563C24×C3—428no—
564C24×C3—424no—
565C24×C3—428no—
566C22⋊A4—72no—
567C22⋊A4(C22⋊D7)⋊C311yescharacteristic, complemented
568C22×A4—41no—
569C22×A4—82no—
570C22×A4—281no—
571C22×A4—282no—
572C22×A4—282no—
573C22×A4—564no—
574C2×C3×D4—421no—
575C2×C3×D4—421no—
576C2×C3×D4—421no—
577C2×C3×D4—422no—
578C2×C3×D4—422no—
579C2×C3×D4—422no—
580C2×C3×D4—424no—
581C2×C3×D4—421no—
582C22×C3×C4—71no—
583C22×C3×C4—211no—
584C22×C3×C4—211no—
585C4×A4—281no—
586C4×A4—282no—
587C3×C22⋊C4—422no—
588C3×C22⋊C4—422no—
589C3×C22⋊C4—421no—
590C3×C22⋊C4—424no—
591C3×C22⋊C4—422no—
592C3×C22⋊C4—421no—
593C3×C22⋊C4—421no—
594C3×C22⋊C4—421no—
595C2×C3×C7—161no—
596C2×C3×C7—321no—
597C3×D7—321no—
598C2×ΓL(1,𝔽8)—21no—
599C2×ΓL(1,𝔽8)—31no—
600C2×ΓL(1,𝔽8)—31no—
601C2×ΓL(1,𝔽8)—62no—
602C2×ΓL(1,𝔽8)—64no—
603C2×ΓL(1,𝔽8)—62no—
604C2×ΓL(1,𝔽8)—61no—
605C2×ΓL(1,𝔽8)—162no—
606C2×ΓL(1,𝔽8)—322no—
607C2×ΓL(1,𝔽8)C2×#120⋊C311yescharacteristic
608AGL(1,𝔽7)—81no—
609AGL(1,𝔽7)—322no—
610C22×C32—1121no—
611C22×C32—1121no—
612C3×A4—281no—
613C3×A4—562no—
614C32×C4—1121no—
615C25—21no—
616C25—31no—
617C25—31no—
618C25—62no—
619C25—62no—
620C25—64no—
621C25—61no—
622C25C2×C3×AGL(1,𝔽7)11yescharacteristic
623C22×D4—71no—
624C22×D4—211no—
625C22×D4—211no—
626#120—141no—
627#120—422no—
628#120—424no—
629#120—422no—
630#120—421no—
631C2×C22⋊C4—211no—
632C2×C22⋊C4—211no—
633C2×C22⋊C4—212no—
634C2×C22⋊C4—211no—
635C2×C22⋊C4—211no—
636C2×C22⋊C4—211no—
637C22×C7—22no—
638C22×C7—31no—
639C22×C7—31no—
640C22×C7—32no—
641C22×C7—32no—
642C22×C7—34no—
643C22×C7—31no—
644C22×C7—61no—
645C22×C7—61no—
646C22×C7—64no—
647C22×C7—64no—
648C22×C7—61no—
649C22×C7—61no—
650C22×C7—62no—
651C22×C7—64no—
652C22×C7—62no—
653C22×C7—62no—
654C22×C7—64no—
655C22×C7—62no—
656C22×C7—64no—
657C22×C7—64no—
658C22×C7—62no—
659C22×C7—62no—
660C22×C7—62no—
661C22×C7—64no—
662C22×C7—64no—
663C22×C7—64no—
664C22×C7—64no—
665C22×C7—68no—
666C22×C7—68no—
667C22×C7—64no—
668C22×C7—68no—
669C22×C7—68no—
670C22×C7—64no—
671C22×C7—62no—
672C22×C7—62no—
673C22×C7C3×#120⋊C311yescharacteristic, complemented
674C22×C7C3×D4×A411yescharacteristic
675C2×D7—41no—
676C2×D7—121no—
677C2×D7—121no—
678Dic7—41no—
679Dic7—121no—
680Dic7—121no—
681C23×C3—71no—
682C23×C3—141no—
683C23×C3—142no—
684C23×C3—144no—
685C23×C3—141no—
686C23×C3—211no—
687C23×C3—211no—
688C23×C3—211no—
689C23×C3—212no—
690C23×C3—212no—
691C23×C3—212no—
692C23×C3—214no—
693C23×C3—211no—
694C23×C3—422no—
695C23×C3—421no—
696C23×C3—422no—
697C23×C3—422no—
698C23×C3—424no—
699C23×C3—421no—
700C23×C3—422no—
701C23×C3—422no—
702C23×C3—422no—
703C23×C3—424no—
704C23×C3—422no—
705C23×C3—421no—
706C23×C3—422no—
707C23×C3—422no—
708C23×C3—424no—
709C23×C3—422no—
710C23×C3—422no—
711C23×C3—424no—
712C23×C3—428no—
713C23×C3—422no—
714C23×C3—424no—
715C23×C3—424no—
716C23×C3—424no—
717C23×C3—428no—
718C23×C3—422no—
719C23×C3—424no—
720C23×C3—422no—
721C23×C3—422no—
722C23×C3—422no—
723C23×C3—424no—
724C23×C3—424no—
725C23×C3—424no—
726C23×C3—424no—
727C23×C3—428no—
728C23×C3—424no—
729C23×C3—424no—
730C23×C3—428no—
731C23×C3—424no—
732C23×C3—424no—
733C23×C3—428no—
734C23×C3—424no—
735C23×C3—428no—
736C23×C3—424no—
737C23×C3—428no—
738C23×C3—424no—
739C23×C3—424no—
740C23×C3—428no—
741C23×C3—428no—
742C23×C3—424no—
743C23×C3—428no—
744C23×C3—428no—
745C23×C3—428no—
746C23×C3—428no—
747C23×C3—421no—
748C23×C3—421no—
749C2×A4—41no—
750C2×A4—82no—
751C2×A4—81no—
752C2×A4—84no—
753C2×A4—282no—
754C2×A4—564no—
755C2×A4—562no—
756C2×A4—568no—
757C2×A4—561no—
758C2×A4—562no—
759C3×D4—281no—
760C3×D4—841no—
761C3×D4—842no—
762C3×D4—842no—
763C3×D4—844no—
764C3×D4—1121no—
765C3×D4—1122no—
766C2×C3×C4—421no—
767C2×C3×C4—421no—
768C2×C3×C4—421no—
769C2×C3×C4—421no—
770C2×C3×C4—421no—
771C2×C3×C4—422no—
772C3×C7—161no—
773ΓL(1,𝔽8)—162no—
774ΓL(1,𝔽8)AΣL(1,𝔽64)11yescharacteristic, complemented
775C2×C32—1121no—
776C2×C32—2241no—
777C2×C32—2241no—
778C24—22no—
779C24—31no—
780C24—31no—
781C24—34no—
782C24—32no—
783C24—32no—
784C24—31no—
785C24—62no—
786C24—61no—
787C24—61no—
788C24—64no—
789C24—64no—
790C24—62no—
791C24—62no—
792C24—61no—
793C24—61no—
794C24—62no—
795C24—64no—
796C24—62no—
797C24—64no—
798C24—64no—
799C24—62no—
800C24—62no—
801C24—64no—
802C24—62no—
803C24—64no—
804C24—62no—
805C24—64no—
806C24—64no—
807C24—64no—
808C24—64no—
809C24—68no—
810C24—68no—
811C24—68no—
812C24—64no—
813C24—68no—
814C24—71no—
815C24C3×(C22⋊D7)⋊C311yescharacteristic, complemented
816C24A4×AGL(1,𝔽7)11yescharacteristic
817C2×D4—421no—
818C2×D4—421no—
819C2×D4—421no—
820C2×D4—422no—
821C2×D4—422no—
822C2×D4—422no—
823C2×D4—424no—
824C2×D4—421no—
825C22×C4—71no—
826C22×C4—211no—
827C22×C4—211no—
828C22⋊C4—422no—
829C22⋊C4—422no—
830C22⋊C4—424no—
831C22⋊C4—422no—
832C22⋊C4—421no—
833C22⋊C4—421no—
834C22⋊C4—421no—
835C22⋊C4—421no—
836C2×C7—21no—
837C2×C7—31no—
838C2×C7—31no—
839C2×C7—62no—
840C2×C7—64no—
841C2×C7—62no—
842C2×C7—61no—
843C2×C7C2×C3×#120⋊C311yescharacteristic
844D7—81no—
845C22×C3—71no—
846C22×C3—71no—
847C22×C3—142no—
848C22×C3—161no—
849C22×C3—211no—
850C22×C3—211no—
851C22×C3—211no—
852C22×C3—212no—
853C22×C3—212no—
854C22×C3—214no—
855C22×C3—281no—
856C22×C3—422no—
857C22×C3—422no—
858C22×C3—421no—
859C22×C3—421no—
860C22×C3—424no—
861C22×C3—424no—
862C22×C3—421no—
863C22×C3—421no—
864C22×C3—422no—
865C22×C3—422no—
866C22×C3—422no—
867C22×C3—424no—
868C22×C3—422no—
869C22×C3—424no—
870C22×C3—424no—
871C22×C3—422no—
872C22×C3—424no—
873C22×C3—422no—
874C22×C3—422no—
875C22×C3—424no—
876C22×C3—424no—
877C22×C3—424no—
878C22×C3—424no—
879C22×C3—428no—
880C22×C3—428no—
881C22×C3—424no—
882C22×C3—428no—
883C22×C3—424no—
884C22×C3—428no—
885C22×C3—841no—
886C22×C3—841no—
887C22×C3—1121no—
888C22×C3—1122no—
889C22×C3—1122no—
890A4—41no—
891A4—82no—
892A4—282no—
893A4—564no—
894C3×C4—281no—
895C3×C4—841no—
896C3×C4—841no—
897C3×C4—1121no—
898C3×C4—1122no—
899C32—1121noSylow
900C23—24no—
901C23—22no—
902C23—21no—
903C23—32no—
904C23—34no—
905C23—32no—
906C23—32no—
907C23—31no—
908C23—31no—
909C23—31no—
910C23—31no—
911C23—62no—
912C23—62no—
913C23—64no—
914C23—61no—
915C23—62no—
916C23—61no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—64no—
922C23—62no—
923C23—62no—
924C23—64no—
925C23—68no—
926C23—62no—
927C23—64no—
928C23—64no—
929C23—64no—
930C23—68no—
931C23—62no—
932C23—64no—
933C23—64no—
934C23—62no—
935C23—62no—
936C23—64no—
937C23—62no—
938C23—62no—
939C23—64no—
940C23—64no—
941C23—68no—
942C23—64no—
943C23—64no—
944C23—68no—
945C23—64no—
946C23—64no—
947C23—68no—
948C23—64no—
949C23—68no—
950C23—64no—
951C23—68no—
952C23—64no—
953C23—64no—
954C23—68no—
955C23—68no—
956C23—64no—
957C23—68no—
958C23—68no—
959C23—68no—
960C23—68no—
961C23—64no—
962C23—61no—
963C23—62no—
964C23—141no—
965C23—421no—
966C23—421no—
967C23C2×A4×AGL(1,𝔽7)11yescharacteristic
968D4—281no—
969D4—841no—
970D4—842no—
971D4—842no—
972D4—844no—
973C2×C4—421no—
974C2×C4—421no—
975C2×C4—422no—
976C2×C4—421no—
977C2×C4—421no—
978C2×C4—421no—
979C7C3×AΣL(1,𝔽64)11yescharacteristic, complemented, Sylow
980C2×C3—71no—
981C2×C3—141no—
982C2×C3—161no—
983C2×C3—211no—
984C2×C3—211no—
985C2×C3—321no—
986C2×C3—422no—
987C2×C3—421no—
988C2×C3—422no—
989C2×C3—424no—
990C2×C3—561no—
991C2×C3—1122no—
992C2×C3—2242no—
993C2×C3—2241no—
994C2×C3—2242no—
995C22—22no—
996C22—31no—
997C22—31no—
998C22—32no—
999C22—32no—
1000C22—34no—
1001C22—31no—
1002C22—61no—
1003C22—61no—
1004C22—64no—
1005C22—64no—
1006C22—61no—
1007C22—61no—
1008C22—62no—
1009C22—64no—
1010C22—62no—
1011C22—62no—
1012C22—64no—
1013C22—62no—
1014C22—64no—
1015C22—64no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—64no—
1020C22—64no—
1021C22—64no—
1022C22—64no—
1023C22—68no—
1024C22—68no—
1025C22—64no—
1026C22—68no—
1027C22—68no—
1028C22—64no—
1029C22—62no—
1030C22—62no—
1031C22—281no—
1032C22—841no—
1033C22—841no—
1034C22#7221460611yescharacteristic, complemented
1035C22A4×(C22⋊D7)⋊C311yescharacteristic
1036C4—281no—
1037C4—841no—
1038C4—841no—
1039C3—71no—
1040C3—161no—
1041C3—1122no—
1042C2—21no—
1043C2—31no—
1044C2—31no—
1045C2—62no—
1046C2—64no—
1047C2—62no—
1048C2—61no—
1049C2—561no—
1050C2C2×#7221460611yescharacteristic
subgroupG/H
centerC2C2×#72214606
commutator, cosocleC25×C7C22×C32
FrattiniC23C2×A4×AGL(1,𝔽7)
FittingC26×C7C2×C32
socleC23×C7C22×C3×A4
hypercenterC22#72214606
hypocenterC24×C7C32×D4
LCSG ▷ C25×C7 ▷ C24×C7
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. #72277753C3semidirect
2. #72277737C3semidirect
3. #72276787C2semidirect
4. C2×#72214606C2semidirect
5. #72276534C3semidirect
7. C22×ΓL(1,𝔽8)×C22⋊A4C2semidirect
11. C22×C22⋊(C22⋊ΓL(1,𝔽8))C2×C3semidirect
12. C22×C7×C22⋊A4C2×C3semidirect
13. C26×ΓL(1,𝔽8)C2×C3semidirect
14. C2×#10620804C2×C3semidirect
15. C2×#10620796C2×C3semidirect
18. C2×#10620789C2×C3semidirect
19. #13052184C2×C3semidirect
20. #13052164C2×C3semidirect
23. #13052147C2×C3semidirect
25. ΓL(1,𝔽8)×C22⋊A4D4semidirect
30. #11741573C32semidirect
47. C22×(C22⋊D7)⋊C3A4semidirect
70. C26×C7C2×C32semidirect
73. C2×#6516C2×C32semidirect
76. #90019C2×C32semidirect
80. C22⋊(C22⋊ΓL(1,𝔽8))C3×D4semidirect
81. C7×C22⋊A4C3×D4semidirect
122. C24×ΓL(1,𝔽8)C3×D4semidirect
126. C23×AGL(1,𝔽7)C2×A4semidirect
139. C22×ΓL(1,𝔽8)⋊C4C2×A4semidirect
167. C22×C22⋊D7C3×A4semidirect
181. C22×C22⋊A4AGL(1,𝔽7)semidirect
328. C24×C7C32×D4semidirect
330. C23×D7C2×C3×A4semidirect
341. C22×Dic7C2×C3×A4semidirect
423. C22×ΓL(1,𝔽8)#120⋊C3semidirect
440. C26C3×AGL(1,𝔽7)semidirect
567. C22⋊A4(C22⋊D7)⋊C3semidirect
673. C22×C7C3×#120⋊C3semidirect
774. ΓL(1,𝔽8)AΣL(1,𝔽64)semidirect
815. C24C3×(C22⋊D7)⋊C3semidirect
979. C7C3×AΣL(1,𝔽64)semidirect
1034. C22#72214606semidirect

Maximal subgroups

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

subgroupindex
#722777533
#722777373
#722767872
C2×#722146062
#722765343
A4×(C22⋊D7)⋊C34
C22×ΓL(1,𝔽8)×C22⋊A42
C3×AΣL(1,𝔽64)7