Finite Group Databasebeta

← #72277159

Subgroups — #72277159

Order 2688.

1600 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6548⋊C3C211yesmaximal, characteristic, complemented
2ΓL(1,𝔽8)×#534C211yesmaximal, characteristic, complemented
3#90495⋊C3C212yesmaximal, complemented
4C2×#6408⋊C3C211yesmaximal, characteristic, complemented
5#89825⋊C3C214yesmaximal, complemented
6#89804⋊C3C214yesmaximal, complemented
7C2×#6380⋊C3C212yesmaximal, complemented
8#11740820C311yesmaximal, characteristic, complemented, Hall
9C22×D4×ΓL(1,𝔽8)C2211yescharacteristic
10C22×D4×ΓL(1,𝔽8)C2211yescharacteristic, complemented
11C22×(C22⋊D7)⋊C3—21no—
12C22×(C22⋊D7)⋊C3C2212yes—
13#6548⋊C3—22no—
14#6548⋊C3—24no—
15#6548⋊C3C2214yes—
16C2×#1159⋊C3—22no—
17C2×D4×AGL(1,𝔽7)—22no—
18C2×#1157⋊C3—21no—
19ΓL(1,𝔽8)×#123—21no—
20ΓL(1,𝔽8)×#123C2212yescomplemented
21ΓL(1,𝔽8)×#121—22no—
22ΓL(1,𝔽8)×#120—21no—
23ΓL(1,𝔽8)×#120C2212yescomplemented
24C2×C22⋊C4×ΓL(1,𝔽8)C2211yescharacteristic, complemented
25#10620789C2214yescomplemented
26C2×(C22⋊Dic7)⋊C3C2212yescomplemented
27#6502⋊C3—24no—
28#6500⋊C3—22no—
29#6498⋊C3—22no—
30#6492⋊C3C2214yescomplemented
31#6408⋊C3C2214yescomplemented
32#6380⋊C3C2218yescomplemented
33C2×#6548C2×C311yescharacteristic, complemented
34C7×#534C2×C311yescharacteristic, complemented
35#90495C2×C312yescomplemented
36C2×#6408C2×C311yescharacteristic, complemented
37#89825C2×C314yescomplemented
38#89804C2×C314yescomplemented
39C2×#6380C2×C312yescomplemented
40C3×#3026—71nomaximal, Hall
41C24×ΓL(1,𝔽8)D411yescharacteristic, complemented
42C24×ΓL(1,𝔽8)C2311yescharacteristic
43C24×ΓL(1,𝔽8)C2311yescharacteristic, complemented
44C23×AGL(1,𝔽7)—21no—
45C23×AGL(1,𝔽7)D412yescomplemented
46C2×D4×ΓL(1,𝔽8)—22no—
47C2×D4×ΓL(1,𝔽8)—22no—
48C2×D4×ΓL(1,𝔽8)—22no—
49C2×D4×ΓL(1,𝔽8)—22no—
50C2×D4×ΓL(1,𝔽8)—21no—
51C2×D4×ΓL(1,𝔽8)—21no—
52C2×D4×ΓL(1,𝔽8)—22no—
53C2×D4×ΓL(1,𝔽8)D412yescomplemented
54C2×D4×ΓL(1,𝔽8)C2312yes—
55C22×C4×ΓL(1,𝔽8)—21no—
56C22×C4×ΓL(1,𝔽8)D411yescharacteristic, complemented
57C22×C4×ΓL(1,𝔽8)C2311yescharacteristic, complemented
58C2×(C22⋊D7)⋊C3—22no—
59C2×(C22⋊D7)⋊C3—24no—
60C2×(C22⋊D7)⋊C3—22no—
61C2×(C22⋊D7)⋊C3—22no—
62C2×(C22⋊D7)⋊C3—22no—
63C2×(C22⋊D7)⋊C3—22no—
64C2×(C22⋊D7)⋊C3—24no—
65C2×(C22⋊D7)⋊C3—24no—
66C2×(C22⋊D7)⋊C3D414yescomplemented
67C2×(C22⋊D7)⋊C3C2314yes—
68C22×ΓL(1,𝔽8)⋊C4—21no—
69C22×ΓL(1,𝔽8)⋊C4—22no—
70C22×ΓL(1,𝔽8)⋊C4D412yescomplemented
71#1159⋊C3—28no—
72#1159⋊C3—28no—
73D4×AGL(1,𝔽7)—28no—
74D4×AGL(1,𝔽7)—28no—
75#1157⋊C3—24no—
76#1157⋊C3—24no—
77C2×C4⋊AGL(1,𝔽7)—21no—
78C2×C4×AGL(1,𝔽7)—22no—
79C2×ΓL(1,𝔽8)⋊Q8—21no—
80C4⋊C4×ΓL(1,𝔽8)—22no—
81C22⋊C4×ΓL(1,𝔽8)—21no—
82C22⋊C4×ΓL(1,𝔽8)—22no—
83C22⋊C4×ΓL(1,𝔽8)—22no—
84C22⋊C4×ΓL(1,𝔽8)C2312yescomplemented
85(C22⋊Dic7)⋊C3—22no—
86(C22⋊Dic7)⋊C3—24no—
87(C22⋊Dic7)⋊C3C2314yescomplemented
88(C2×AGL(1,𝔽7))⋊C4—24no—
89(ΓL(1,𝔽8)⋊C4)⋊C4—24no—
90C22×C7×D4C22×C311yescharacteristic
91C22×C7×D4C22×C311yescharacteristic, complemented
92C22×C22⋊D7—21no—
93C22×C22⋊D7C22×C312yes—
94#6548—22no—
95#6548—24no—
96#6548C22×C314yes—
97C2×#1159—22no—
98C2×D4×D7—22no—
99C2×#1157—21no—
100C7×#123—21no—
101C7×#123C22×C312yescomplemented
102C7×#121—22no—
103C7×#120—21no—
104C7×#120C22×C312yescomplemented
105C2×C7×C22⋊C4C22×C311yescharacteristic, complemented
106#6516C22×C314yescomplemented
107C2×C22⋊Dic7C22×C312yescomplemented
108#6502—24no—
109#6500—22no—
110#6498—22no—
111#6492C22×C314yescomplemented
112#6408C22×C314yescomplemented
113#6380C22×C318yescomplemented
114C2×C3×H(5,𝔽2)—71no—
115C3×#534—72no—
116C3×#534—71no—
117C3×#458—74no—
118C3×B(4,𝔽2)—74no—
119C2×C3×#99—72no—
120C2×C3×#99—71no—
121C23×ΓL(1,𝔽8)—21no—
122C23×ΓL(1,𝔽8)—21no—
123C23×ΓL(1,𝔽8)—21no—
124C23×ΓL(1,𝔽8)—22no—
125C23×ΓL(1,𝔽8)—81no—
126C23×ΓL(1,𝔽8)—81no—
127C23×ΓL(1,𝔽8)—81no—
128C23×ΓL(1,𝔽8)C2×D412yes—
129C23×ΓL(1,𝔽8)C2×D411yescharacteristic
130C23×ΓL(1,𝔽8)C2×D412yes—
131C23×ΓL(1,𝔽8)C2×D412yes—
132C23×ΓL(1,𝔽8)C2×D411yescharacteristic
133C23×ΓL(1,𝔽8)C2411yescharacteristic
134C22×AGL(1,𝔽7)—22no—
135C22×AGL(1,𝔽7)—24no—
136C22×AGL(1,𝔽7)—22no—
137C22×AGL(1,𝔽7)—82no—
138C22×AGL(1,𝔽7)—82no—
139C22×AGL(1,𝔽7)C2×D414yes—
140D4×ΓL(1,𝔽8)—24no—
141D4×ΓL(1,𝔽8)—24no—
142D4×ΓL(1,𝔽8)—41no—
143D4×ΓL(1,𝔽8)—42no—
144D4×ΓL(1,𝔽8)—41no—
145D4×ΓL(1,𝔽8)—82no—
146C2×C4×ΓL(1,𝔽8)—21no—
147C2×C4×ΓL(1,𝔽8)—21no—
148C2×C4×ΓL(1,𝔽8)—22no—
149C2×C4×ΓL(1,𝔽8)—21no—
150C2×C4×ΓL(1,𝔽8)—22no—
151C2×C4×ΓL(1,𝔽8)—81no—
152C2×C4×ΓL(1,𝔽8)C2×D412yes—
153(C22⋊D7)⋊C3—28no—
154(C22⋊D7)⋊C3—24no—
155(C22⋊D7)⋊C3—24no—
156(C22⋊D7)⋊C3—24no—
157(C22⋊D7)⋊C3—24no—
158(C22⋊D7)⋊C3—84no—
159C2×ΓL(1,𝔽8)⋊C4—24no—
160C2×ΓL(1,𝔽8)⋊C4—22no—
161C2×ΓL(1,𝔽8)⋊C4—22no—
162C2×ΓL(1,𝔽8)⋊C4—24no—
163C2×ΓL(1,𝔽8)⋊C4—82no—
164C2×ΓL(1,𝔽8)⋊C4C2×D414yes—
165C4⋊AGL(1,𝔽7)—24no—
166C4×AGL(1,𝔽7)—28no—
167ΓL(1,𝔽8)⋊Q8—24no—
168#3026—71noSylow
169C24×C7C3×D411yescharacteristic, complemented
170C24×C7C23×C311yescharacteristic
171C24×C7C23×C311yescharacteristic, complemented
172C23×D7—21no—
173C23×D7C3×D412yescomplemented
174C2×C7×D4—22no—
175C2×C7×D4—22no—
176C2×C7×D4—22no—
177C2×C7×D4—22no—
178C2×C7×D4—21no—
179C2×C7×D4—21no—
180C2×C7×D4—22no—
181C2×C7×D4C3×D412yescomplemented
182C2×C7×D4C23×C312yes—
183C22×C4×C7—21no—
184C22×C4×C7C3×D411yescharacteristic, complemented
185C22×C4×C7C23×C311yescharacteristic, complemented
186C2×C22⋊D7—22no—
187C2×C22⋊D7—24no—
188C2×C22⋊D7—22no—
189C2×C22⋊D7—22no—
190C2×C22⋊D7—22no—
191C2×C22⋊D7—22no—
192C2×C22⋊D7—24no—
193C2×C22⋊D7—24no—
194C2×C22⋊D7C3×D414yescomplemented
195C2×C22⋊D7C23×C314yes—
196C22×Dic7—21no—
197C22×Dic7—22no—
198C22×Dic7C3×D412yescomplemented
199#1159—28no—
200#1159—28no—
201D4×D7—28no—
202D4×D7—28no—
203#1157—24no—
204#1157—24no—
205C2×D28—21no—
206C2×C4×D7—22no—
207C2×Dic14—21no—
208C7×C4⋊C4—22no—
209C7×C22⋊C4—21no—
210C7×C22⋊C4—22no—
211C7×C22⋊C4—22no—
212C7×C22⋊C4C23×C312yescomplemented
213C22⋊Dic7—22no—
214C22⋊Dic7—24no—
215C22⋊Dic7C23×C314yescomplemented
216(C2×D7)⋊C4—24no—
217Dic7⋊C4—24no—
218C3×H(5,𝔽2)—74no—
219C3×H(5,𝔽2)—144no—
220C3×H(5,𝔽2)—142no—
221C2×C3×#41—141no—
222C2×C3×#41—142no—
223C22×C3×D4—72no—
224C22×C3×D4—71no—
225C22×C3×D4—71no—
226C22×C3×D4—142no—
227C22×C3×D4—141no—
228C3×#123—74no—
229C3×#123—72no—
230C3×#123—141no—
231C3×#123—142no—
232C3×#121—142no—
233C3×#121—144no—
234C3×#120—74no—
235C3×#120—72no—
236C3×#120—141no—
237C3×#120—142no—
238C2×C3×C22⋊C4—72no—
239C2×C3×C22⋊C4—71no—
240C3×#99—78no—
241C3×#99—74no—
242C22×ΓL(1,𝔽8)—22no—
243C22×ΓL(1,𝔽8)—42no—
244C22×ΓL(1,𝔽8)—41no—
245C22×ΓL(1,𝔽8)—42no—
246C22×ΓL(1,𝔽8)—41no—
247C22×ΓL(1,𝔽8)—41no—
248C22×ΓL(1,𝔽8)—42no—
249C22×ΓL(1,𝔽8)—42no—
250C22×ΓL(1,𝔽8)—44no—
251C22×ΓL(1,𝔽8)—42no—
252C22×ΓL(1,𝔽8)—41no—
253C22×ΓL(1,𝔽8)—81no—
254C22×ΓL(1,𝔽8)#12011yescharacteristic
255C22×ΓL(1,𝔽8)#12012yes—
256C22×ΓL(1,𝔽8)#12011yescharacteristic
257C22×ΓL(1,𝔽8)C22×D412yes—
258C22×ΓL(1,𝔽8)C22×D411yescharacteristic
259C2×AGL(1,𝔽7)—24no—
260C2×AGL(1,𝔽7)—44no—
261C2×AGL(1,𝔽7)—44no—
262C2×AGL(1,𝔽7)—82no—
263C2×AGL(1,𝔽7)—84no—
264C4×ΓL(1,𝔽8)—22no—
265C4×ΓL(1,𝔽8)—42no—
266C4×ΓL(1,𝔽8)—41no—
267ΓL(1,𝔽8)⋊C4—24no—
268ΓL(1,𝔽8)⋊C4—44no—
269C2×H(5,𝔽2)—71no—
270#534—72no—
271#534AGL(1,𝔽7)11yescharacteristic, complemented
272#458—74no—
273B(4,𝔽2)—74no—
274C2×#99—71no—
275C2×#99—72no—
276C23×C7—21no—
277C23×C7—21no—
278C23×C7—22no—
279C23×C7—21no—
280C23×C7—81no—
281C23×C7—81no—
282C23×C7—81no—
283C23×C7C2×C3×D412yes—
284C23×C7C2×C3×D412yes—
285C23×C7C2×C3×D412yes—
286C23×C7C2×C3×D411yescharacteristic
287C23×C7C2×C3×D411yescharacteristic
288C23×C7C24×C311yescharacteristic
289C22×D7—22no—
290C22×D7—24no—
291C22×D7—22no—
292C22×D7—82no—
293C22×D7—82no—
294C22×D7C2×C3×D414yes—
295C7×D4—24no—
296C7×D4—24no—
297C7×D4—41no—
298C7×D4—42no—
299C7×D4—41no—
300C7×D4—82no—
301C2×C4×C7—21no—
302C2×C4×C7—21no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—21no—
306C2×C4×C7—81no—
307C2×C4×C7C2×C3×D412yes—
308C22⋊D7—28no—
309C22⋊D7—24no—
310C22⋊D7—24no—
311C22⋊D7—24no—
312C22⋊D7—24no—
313C22⋊D7—84no—
314C2×Dic7—24no—
315C2×Dic7—22no—
316C2×Dic7—22no—
317C2×Dic7—24no—
318C2×Dic7—82no—
319C2×Dic7C2×C3×D414yes—
320D28—24no—
321C4×D7—28no—
322Dic14—24no—
323C24×C3—72no—
324C24×C3—71no—
325C24×C3—71no—
326C24×C3—71no—
327C24×C3—141no—
328C3×#41—144no—
329C3×#41—148no—
330C3×#41—144no—
331C3×#41—148no—
332C2×C3×Q8—141no—
333C2×C3×D4—74no—
334C2×C3×D4—74no—
335C2×C3×D4—72no—
336C2×C3×D4—72no—
337C2×C3×D4—142no—
338C2×C3×D4—142no—
339C2×C3×D4—142no—
340C2×C3×D4—141no—
341C2×C3×D4—142no—
342C2×C3×D4—141no—
343C2×C3×D4—142no—
344C2×C3×D4—148no—
345C2×C3×D4—142no—
346C2×C3×D4—142no—
347C2×C3×D4—142no—
348C2×C3×D4—142no—
349C2×C3×D4—144no—
350C2×C3×D4—141no—
351C2×C3×D4—148no—
352C2×C3×D4—142no—
353C2×C3×D4—144no—
354C2×C3×D4—144no—
355C22×C3×C4—72no—
356C22×C3×C4—71no—
357C22×C3×C4—71no—
358C22×C3×C4—141no—
359C22×C3×C4—142no—
360C22×C3×C4—141no—
361C22×C3×C4—142no—
362C3×C4⋊C4—142no—
363C3×C4⋊C4—144no—
364C3×C22⋊C4—74no—
365C3×C22⋊C4—72no—
366C3×C22⋊C4—142no—
367C3×C22⋊C4—141no—
368C3×C22⋊C4—142no—
369C3×C22⋊C4—144no—
370C3×C22⋊C4—142no—
371C3×C22⋊C4—144no—
372C2×ΓL(1,𝔽8)—22no—
373C2×ΓL(1,𝔽8)—21no—
374C2×ΓL(1,𝔽8)—21no—
375C2×ΓL(1,𝔽8)—22no—
376C2×ΓL(1,𝔽8)—21no—
377C2×ΓL(1,𝔽8)—42no—
378C2×ΓL(1,𝔽8)—81no—
379C2×ΓL(1,𝔽8)C2×#12011yescharacteristic
380AGL(1,𝔽7)—44no—
381H(5,𝔽2)—74no—
382H(5,𝔽2)—144no—
383H(5,𝔽2)—142no—
384C2×#41—142no—
385C2×#41—141no—
386C22×D4—72no—
387C22×D4—142no—
388C22×D4—141no—
389C22×D4C2×AGL(1,𝔽7)11yescharacteristic
390C22×D4C2×AGL(1,𝔽7)11yescharacteristic, complemented
391#123—21no—
392#123—74no—
393#123—142no—
394#123C2×AGL(1,𝔽7)12yescomplemented
395#121—22no—
396#121—144no—
397#120—21no—
398#120—74no—
399#120—142no—
400#120C2×AGL(1,𝔽7)12yescomplemented
401C2×C22⋊C4—72no—
402C2×C22⋊C4C2×AGL(1,𝔽7)11yescharacteristic, complemented
403#99—74no—
404#99—78no—
405C22×C7—22no—
406C22×C7—42no—
407C22×C7—41no—
408C22×C7—42no—
409C22×C7—41no—
410C22×C7—41no—
411C22×C7—42no—
412C22×C7—42no—
413C22×C7—44no—
414C22×C7—42no—
415C22×C7—41no—
416C22×C7—81no—
417C22×C7C3×#12011yescharacteristic
418C22×C7C3×#12012yes—
419C22×C7C3×#12011yescharacteristic
420C22×C7C22×C3×D412yes—
421C22×C7C22×C3×D411yescharacteristic
422C2×D7—24no—
423C2×D7—44no—
424C2×D7—44no—
425C2×D7—82no—
426C2×D7—84no—
427C4×C7—22no—
428C4×C7—42no—
429C4×C7—41no—
430Dic7—24no—
431Dic7—44no—
432C23×C3—74no—
433C23×C3—72no—
434C23×C3—72no—
435C23×C3—71no—
436C23×C3—71no—
437C23×C3—72no—
438C23×C3—71no—
439C23×C3—141no—
440C23×C3—141no—
441C23×C3—142no—
442C23×C3—141no—
443C23×C3—142no—
444C23×C3—142no—
445C23×C3—144no—
446C23×C3—561no—
447C23×C3—561no—
448C23×C3—561no—
449C23×C3—562no—
450C23×C3—562no—
451C3×Q8—144no—
452C3×D4—144no—
453C3×D4—144no—
454C3×D4—144no—
455C3×D4—144no—
456C3×D4—144no—
457C3×D4—144no—
458C3×D4—144no—
459C3×D4—148no—
460C3×D4—281no—
461C3×D4—281no—
462C3×D4—282no—
463C3×D4—562no—
464C3×D4—564no—
465C2×C3×C4—74no—
466C2×C3×C4—72no—
467C2×C3×C4—141no—
468C2×C3×C4—141no—
469C2×C3×C4—142no—
470C2×C3×C4—142no—
471C2×C3×C4—141no—
472C2×C3×C4—142no—
473C2×C3×C4—142no—
474C2×C3×C4—148no—
475C2×C3×C4—144no—
476C2×C3×C4—144no—
477C2×C3×C4—561no—
478C2×C3×C4—562no—
479ΓL(1,𝔽8)#302611yescharacteristic, complemented, Hall
480C24—72no—
481C24—141no—
482C24(C22⋊D7)⋊C311yescharacteristic, complemented
483C24C22×AGL(1,𝔽7)11yescharacteristic
484C24C22×AGL(1,𝔽7)11yescharacteristic, complemented
485#41—144no—
486#41—148no—
487#41—148no—
488#41—144no—
489C2×Q8—141no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—22no—
497C2×D4—74no—
498C2×D4—74no—
499C2×D4—141no—
500C2×D4—148no—
501C2×D4—148no—
502C2×D4—142no—
503C2×D4—144no—
504C2×D4—142no—
505C2×D4—142no—
506C2×D4—142no—
507C2×D4—142no—
508C2×D4—144no—
509C2×D4—144no—
510C2×D4(C22⋊D7)⋊C312yescomplemented
511C2×D4C22×AGL(1,𝔽7)12yes—
512C22×C4—21no—
513C22×C4—72no—
514C22×C4—142no—
515C22×C4—141no—
516C22×C4—142no—
517C22×C4(C22⋊D7)⋊C311yescharacteristic, complemented
518C22×C4C22×AGL(1,𝔽7)11yescharacteristic, complemented
519C4⋊C4—22no—
520C4⋊C4—144no—
521C22⋊C4—21no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—74no—
525C22⋊C4—144no—
526C22⋊C4—144no—
527C22⋊C4—142no—
528C22⋊C4C22×AGL(1,𝔽7)12yescomplemented
529C2×C7—22no—
530C2×C7—21no—
531C2×C7—21no—
532C2×C7—22no—
533C2×C7—21no—
534C2×C7—42no—
535C2×C7—81no—
536C2×C7C2×C3×#12011yescharacteristic
537D7—44no—
538C22×C3—72no—
539C22×C3—71no—
540C22×C3—71no—
541C22×C3—71no—
542C22×C3—72no—
543C22×C3—142no—
544C22×C3—144no—
545C22×C3—281no—
546C22×C3—281no—
547C22×C3—282no—
548C22×C3—281no—
549C22×C3—281no—
550C22×C3—282no—
551C22×C3—282no—
552C22×C3—282no—
553C22×C3—282no—
554C22×C3—284no—
555C22×C3—284no—
556C22×C3—284no—
557C22×C3—561no—
558C22×C3—562no—
559C22×C3—564no—
560C3×C4—142no—
561C3×C4—144no—
562C3×C4—281no—
563C3×C4—282no—
564C3×C4—284no—
565C23—21no—
566C23—21no—
567C23—22no—
568C23—21no—
569C23—74no—
570C23—81no—
571C23—81no—
572C23—81no—
573C23—144no—
574C23—142no—
575C23—142no—
576C23—562no—
577C23—562no—
578C23D4×AGL(1,𝔽7)12yes—
579C23D4×AGL(1,𝔽7)12yes—
580C23C2×(C22⋊D7)⋊C312yes—
581C23C2×(C22⋊D7)⋊C311yescharacteristic
582C23C2×(C22⋊D7)⋊C311yescharacteristic
583C23C23×AGL(1,𝔽7)11yescharacteristic
584Q8—144no—
585D4—24no—
586D4—24no—
587D4—41no—
588D4—41no—
589D4—42no—
590D4—82no—
591D4—144no—
592D4—148no—
593D4—144no—
594D4—144no—
595D4—144no—
596D4—144no—
597D4—564no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—74no—
604C2×C4—81no—
605C2×C4—148no—
606C2×C4—144no—
607C2×C4—142no—
608C2×C4—142no—
609C2×C4—144no—
610C2×C4—562no—
611C2×C4C2×(C22⋊D7)⋊C312yes—
612C7C3×#302611yescharacteristic, complemented, Sylow
613C2×C3—71no—
614C2×C3—141no—
615C2×C3—142no—
616C2×C3—141no—
617C2×C3—141no—
618C2×C3—142no—
619C2×C3—282no—
620C2×C3—284no—
621C2×C3—561no—
622C22—22no—
623C22—41no—
624C22—42no—
625C22—41no—
626C22—41no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—44no—
632C22—41no—
633C22—81no—
634C22—144no—
635C22—284no—
636C22—284no—
637C22—562no—
638C22—564no—
639C22#6500⋊C311yescharacteristic
640C22#6500⋊C311yescharacteristic
641C22#6500⋊C312yes—
642C22C2×D4×AGL(1,𝔽7)12yes—
643C22C22×(C22⋊D7)⋊C311yescharacteristic
644C4—22no—
645C4—42no—
646C4—41no—
647C4—144no—
648C4—284no—
649C3—71noSylow
650C2—21no—
651C2—22no—
652C2—21no—
653C2—21no—
654C2—22no—
655C2—42no—
656C2—81no—
657C2—284no—
658C2C2×#6500⋊C311yescharacteristic
subgroupG/H
centerC2C2×#6500⋊C3
commutator, cosocleC23×C7C24×C3
FrattiniC23C23×AGL(1,𝔽7)
FittingC7×#534C2×C3
socleC2×C7C2×C3×#120
hypercenter#534AGL(1,𝔽7)
hypocenterC7C3×#3026
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C2×#6548⋊C3C2semidirect
2. ΓL(1,𝔽8)×#534C2semidirect
3. #90495⋊C3C2semidirect
4. C2×#6408⋊C3C2semidirect
5. #89825⋊C3C2semidirect
6. #89804⋊C3C2semidirect
7. C2×#6380⋊C3C2semidirect
8. #11740820C3semidirect
10. C22×D4×ΓL(1,𝔽8)C22semidirect
20. ΓL(1,𝔽8)×#123C22semidirect
23. ΓL(1,𝔽8)×#120C22semidirect
24. C2×C22⋊C4×ΓL(1,𝔽8)C22semidirect
25. #10620789C22semidirect
26. C2×(C22⋊Dic7)⋊C3C22semidirect
30. #6492⋊C3C22semidirect
31. #6408⋊C3C22semidirect
32. #6380⋊C3C22semidirect
33. C2×#6548C2×C3semidirect
34. C7×#534C2×C3semidirect
35. #90495C2×C3semidirect
36. C2×#6408C2×C3semidirect
37. #89825C2×C3semidirect
38. #89804C2×C3semidirect
39. C2×#6380C2×C3semidirect
41. C24×ΓL(1,𝔽8)D4semidirect
43. C24×ΓL(1,𝔽8)C23semidirect
45. C23×AGL(1,𝔽7)D4semidirect
53. C2×D4×ΓL(1,𝔽8)D4semidirect
56. C22×C4×ΓL(1,𝔽8)D4semidirect
57. C22×C4×ΓL(1,𝔽8)C23semidirect
66. C2×(C22⋊D7)⋊C3D4semidirect
70. C22×ΓL(1,𝔽8)⋊C4D4semidirect
84. C22⋊C4×ΓL(1,𝔽8)C23semidirect
87. (C22⋊Dic7)⋊C3C23semidirect
91. C22×C7×D4C22×C3semidirect
101. C7×#123C22×C3semidirect
104. C7×#120C22×C3semidirect
105. C2×C7×C22⋊C4C22×C3semidirect
106. #6516C22×C3semidirect
107. C2×C22⋊Dic7C22×C3semidirect
111. #6492C22×C3semidirect
112. #6408C22×C3semidirect
113. #6380C22×C3semidirect
169. C24×C7C3×D4semidirect
171. C24×C7C23×C3semidirect
173. C23×D7C3×D4semidirect
181. C2×C7×D4C3×D4semidirect
184. C22×C4×C7C3×D4semidirect
185. C22×C4×C7C23×C3semidirect
194. C2×C22⋊D7C3×D4semidirect
198. C22×Dic7C3×D4semidirect
212. C7×C22⋊C4C23×C3semidirect
215. C22⋊Dic7C23×C3semidirect
271. #534AGL(1,𝔽7)semidirect
390. C22×D4C2×AGL(1,𝔽7)semidirect
394. #123C2×AGL(1,𝔽7)semidirect
400. #120C2×AGL(1,𝔽7)semidirect
402. C2×C22⋊C4C2×AGL(1,𝔽7)semidirect
479. ΓL(1,𝔽8)#3026semidirect
482. C24(C22⋊D7)⋊C3semidirect
484. C24C22×AGL(1,𝔽7)semidirect
510. C2×D4(C22⋊D7)⋊C3semidirect
517. C22×C4(C22⋊D7)⋊C3semidirect
518. C22×C4C22×AGL(1,𝔽7)semidirect
528. C22⋊C4C22×AGL(1,𝔽7)semidirect
612. C7C3×#3026semidirect

Maximal subgroups

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

subgroupindex
C2×#6548⋊C32
ΓL(1,𝔽8)×#5342
#90495⋊C32
C2×#6408⋊C32
#89825⋊C32
#89804⋊C32
C2×#6380⋊C32
#117408203
C3×#30267