Finite Group Databasebeta

← #72277042

Subgroups — #72277042

Order 2688.

1176 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10621518C211yesmaximal, characteristic
2ΓL(1,𝔽8)×#421C211yesmaximal, characteristic, complemented
3#90008⋊C3C211yesmaximal, characteristic, complemented
4#89904⋊C3C211yesmaximal, characteristic, complemented
5#89903⋊C3C211yesmaximal, characteristic, complemented
6#89778⋊C3C211yesmaximal, characteristic, complemented
7#89773⋊C3C211yesmaximal, characteristic, complemented
8#11728168C311yesmaximal, characteristic, complemented, Hall
9C2×#41×ΓL(1,𝔽8)C2211yescharacteristic
10#10621518—22no—
11#10621518—22no—
12#10621518—22no—
13#10621518—22no—
14C2×#66659C412yescomplemented
15C2×D4×AGL(1,𝔽7)—22no—
16C2×D4×AGL(1,𝔽7)C412yescomplemented
17C2×#1157⋊C3—21no—
18C2×#1157⋊C3C2211yescharacteristic
19C22×C4⋊AGL(1,𝔽7)—21no—
20C22×C4⋊AGL(1,𝔽7)C2211yescharacteristic
21C2×M16×ΓL(1,𝔽8)C2211yescharacteristic, complemented
22ΓL(1,𝔽8)×#117C2211yescharacteristic, complemented
23#6489⋊C3C2211yescharacteristic, complemented
24C2×#1136⋊C3C2211yescharacteristic, complemented
25ΓL(1,𝔽8)×#104—22no—
26#6411⋊C3—22no—
27#6398⋊C3—21no—
28#6397⋊C3—21no—
29#6395⋊C3—22no—
30#6383⋊C3—22no—
31#6380⋊C3—22no—
32C2×#6553C2×C311yescharacteristic
33C7×#421C2×C311yescharacteristic, complemented
34#90008C2×C311yescharacteristic, complemented
35#89904C2×C311yescharacteristic, complemented
36#89903C2×C311yescharacteristic, complemented
37#89778C2×C311yescharacteristic, complemented
38#89773C2×C311yescharacteristic, complemented
39C3×#1795—71nomaximal, Hall
40C23×AGL(1,𝔽7)—21no—
41C23×AGL(1,𝔽7)—22no—
42#41×ΓL(1,𝔽8)—21no—
43#41×ΓL(1,𝔽8)—21no—
44#41×ΓL(1,𝔽8)D412yes—
45#41×ΓL(1,𝔽8)D412yes—
46C2×Q8×ΓL(1,𝔽8)C2×C411yescharacteristic
47C2×D4×ΓL(1,𝔽8)—21no—
48C2×D4×ΓL(1,𝔽8)C2×C411yescharacteristic
49C22×C4×ΓL(1,𝔽8)—21no—
50C22×C4×ΓL(1,𝔽8)C2311yescharacteristic
51C2×(C22⋊D7)⋊C3—22no—
52C2×(C22⋊D7)⋊C3D412yes—
53#66659—24no—
54#66659—24no—
55D4×AGL(1,𝔽7)—28no—
56D4×AGL(1,𝔽7)—28no—
57D4×AGL(1,𝔽7)—24no—
58D4×AGL(1,𝔽7)—24no—
59#1157⋊C3—24no—
60#1157⋊C3—24no—
61#1157⋊C3—21no—
62#1157⋊C3—21no—
63#1157⋊C3—21no—
64#1157⋊C3—21no—
65C2×C4⋊AGL(1,𝔽7)—24no—
66C2×C4⋊AGL(1,𝔽7)—24no—
67C2×C4⋊AGL(1,𝔽7)—22no—
68C2×C4⋊AGL(1,𝔽7)—21no—
69C2×C4⋊AGL(1,𝔽7)—21no—
70C2×C4⋊AGL(1,𝔽7)—21no—
71C2×C4⋊AGL(1,𝔽7)C2×C412yes—
72C2×C4⋊AGL(1,𝔽7)D411yescharacteristic
73C2×C4⋊AGL(1,𝔽7)D412yes—
74C2×C4⋊AGL(1,𝔽7)D412yes—
75C2×C4×AGL(1,𝔽7)—22no—
76C2×C4×AGL(1,𝔽7)C2×C412yes—
77C2×ΓL(1,𝔽8)⋊Q8D411yescharacteristic
78M16×ΓL(1,𝔽8)—21no—
79M16×ΓL(1,𝔽8)—21no—
80C2×C8×ΓL(1,𝔽8)—21no—
81C4⋊C4×ΓL(1,𝔽8)—21no—
82C22⋊C4×ΓL(1,𝔽8)—21no—
83C42×ΓL(1,𝔽8)—21no—
84(C22⋊Dic7)⋊C3—21no—
85C4⋊(ΓL(1,𝔽8)⋊C4)—21no—
86C4×ΓL(1,𝔽8)⋊C4—21no—
87#1136⋊C3—21no—
88#1136⋊C3—21no—
89C2×ΓL(1,𝔽8)⋊C8—21no—
90C2×C7×#41C22×C311yescharacteristic
91#6553—22no—
92#6553—22no—
93#6553—22no—
94#6553—22no—
95C2×#1161C3×C412yescomplemented
96C2×D4×D7—22no—
97C2×D4×D7C3×C412yescomplemented
98C2×#1157—21no—
99C2×#1157C22×C311yescharacteristic
100C22×D28—21no—
101C22×D28C22×C311yescharacteristic
102C2×C7×M16C22×C311yescharacteristic, complemented
103C7×#117C22×C311yescharacteristic, complemented
104#6489C22×C311yescharacteristic, complemented
105C2×#1136C22×C311yescharacteristic, complemented
106C7×#104—22no—
107#6411—22no—
108#6398—21no—
109#6397—21no—
110#6395—22no—
111#6383—22no—
112#6380—22no—
113C2×C3×H(5,𝔽2)—71no—
114C3×#421—71no—
115C3×#421—71no—
116C3×#418—71no—
117C3×#418—71no—
118C3×#413—71no—
119C3×#410—71no—
120C23×ΓL(1,𝔽8)—21no—
121C23×ΓL(1,𝔽8)C2×D411yescharacteristic
122C22×AGL(1,𝔽7)—22no—
123C22×AGL(1,𝔽7)—28no—
124C22×AGL(1,𝔽7)—22no—
125C22×AGL(1,𝔽7)—22no—
126C22×AGL(1,𝔽7)—82no—
127C22×AGL(1,𝔽7)—84no—
128C22×AGL(1,𝔽7)C22⋊C412yes—
129Q8×ΓL(1,𝔽8)—21no—
130Q8×ΓL(1,𝔽8)C22⋊C412yes—
131D4×ΓL(1,𝔽8)—22no—
132D4×ΓL(1,𝔽8)—22no—
133D4×ΓL(1,𝔽8)—21no—
134D4×ΓL(1,𝔽8)C22⋊C412yes—
135C2×C4×ΓL(1,𝔽8)—21no—
136C2×C4×ΓL(1,𝔽8)—22no—
137C2×C4×ΓL(1,𝔽8)—22no—
138C2×C4×ΓL(1,𝔽8)—41no—
139C2×C4×ΓL(1,𝔽8)C22×C411yescharacteristic
140C2×C4×ΓL(1,𝔽8)C2×D411yescharacteristic
141C2×C4×ΓL(1,𝔽8)C2×D411yescharacteristic
142C2×C4×ΓL(1,𝔽8)C2×D411yescharacteristic
143C2×C4×ΓL(1,𝔽8)C2×D411yescharacteristic
144C2×C4×ΓL(1,𝔽8)C2×D411yescharacteristic
145(C22⋊D7)⋊C3—28no—
146(C22⋊D7)⋊C3—22no—
147(C22⋊D7)⋊C3—22no—
148C2×ΓL(1,𝔽8)⋊C4—41no—
149C2×ΓL(1,𝔽8)⋊C4C22⋊C412yes—
150C4⋊AGL(1,𝔽7)—28no—
151C4⋊AGL(1,𝔽7)—22no—
152C4⋊AGL(1,𝔽7)—21no—
153C4⋊AGL(1,𝔽7)—22no—
154C4⋊AGL(1,𝔽7)—21no—
155C4⋊AGL(1,𝔽7)—22no—
156C4⋊AGL(1,𝔽7)C22⋊C414yes—
157C4×AGL(1,𝔽7)—28no—
158C4×AGL(1,𝔽7)—22no—
159C4×AGL(1,𝔽7)—22no—
160ΓL(1,𝔽8)⋊Q8—21no—
161ΓL(1,𝔽8)⋊Q8—21no—
162C8×ΓL(1,𝔽8)—41no—
163ΓL(1,𝔽8)⋊C8—41no—
164#1795—71noSylow
165C23×D7—21no—
166C23×D7—22no—
167C7×#41—21no—
168C7×#41—21no—
169C7×#41C3×D412yes—
170C7×#41C3×D412yes—
171C2×C7×Q8C2×C3×C411yescharacteristic
172C2×C7×D4—21no—
173C2×C7×D4C2×C3×C411yescharacteristic
174C22×C4×C7—21no—
175C22×C4×C7C23×C311yescharacteristic
176C2×C22⋊D7—22no—
177C2×C22⋊D7C3×D412yes—
178#1161—24no—
179#1161—24no—
180D4×D7—28no—
181D4×D7—28no—
182D4×D7—24no—
183D4×D7—24no—
184#1157—24no—
185#1157—24no—
186#1157—21no—
187#1157—21no—
188#1157—21no—
189#1157—21no—
190C2×D28—24no—
191C2×D28—24no—
192C2×D28—22no—
193C2×D28—21no—
194C2×D28—21no—
195C2×D28—21no—
196C2×D28C2×C3×C412yes—
197C2×D28C3×D411yescharacteristic
198C2×D28C3×D412yes—
199C2×D28C3×D412yes—
200C2×C4×D7—22no—
201C2×C4×D7C2×C3×C412yes—
202C2×Dic14C3×D411yescharacteristic
203C7×M16—21no—
204C7×M16—21no—
205C2×C7×C8—21no—
206C7×C4⋊C4—21no—
207C7×C22⋊C4—21no—
208C42×C7—21no—
209C22⋊Dic7—21no—
210C4⋊Dic7—21no—
211C4×Dic7—21no—
212#1136—21no—
213#1136—21no—
214C2×C7⋊C8—21no—
215C3×H(5,𝔽2)—142no—
216C3×H(5,𝔽2)—142no—
217C3×H(5,𝔽2)—142no—
218C3×H(5,𝔽2)—142no—
219C2×C3×#41—71no—
220C2×C3×#41—72no—
221C2×C3×#41—71no—
222C2×C3×#41—141no—
223C22×C3×D4—71no—
224C22×C3×D4—72no—
225C22×C3×D4—141no—
226C22×C3×D4—142no—
227C2×C3×M16—71no—
228C2×C3×M16—71no—
229C3×#117—71no—
230C3×#117—71no—
231C3×#104—142no—
232C3×#104—142no—
233C3×#102—142no—
234C3×#102—142no—
235C3×#101—141no—
236C3×#100—141no—
237C3×#99—142no—
238C22×ΓL(1,𝔽8)—22no—
239C22×ΓL(1,𝔽8)—41no—
240C22×ΓL(1,𝔽8)—42no—
241C22×ΓL(1,𝔽8)C2×C22⋊C411yescharacteristic
242C22×ΓL(1,𝔽8)#12011yescharacteristic
243C22×ΓL(1,𝔽8)#12011yescharacteristic
244C2×AGL(1,𝔽7)—22no—
245C2×AGL(1,𝔽7)—24no—
246C2×AGL(1,𝔽7)—44no—
247C2×AGL(1,𝔽7)—42no—
248C2×AGL(1,𝔽7)—82no—
249C2×AGL(1,𝔽7)—82no—
250C2×AGL(1,𝔽7)—88no—
251C4×ΓL(1,𝔽8)—22no—
252C4×ΓL(1,𝔽8)—81no—
253C4×ΓL(1,𝔽8)C2×C22⋊C411yescharacteristic
254C4×ΓL(1,𝔽8)C2×C22⋊C411yescharacteristic
255C4×ΓL(1,𝔽8)#12011yescharacteristic
256C4×ΓL(1,𝔽8)#12011yescharacteristic
257ΓL(1,𝔽8)⋊C4—22no—
258ΓL(1,𝔽8)⋊C4—81no—
259C2×H(5,𝔽2)—71no—
260#421—71no—
261#421AGL(1,𝔽7)11yescharacteristic, complemented
262#418—71no—
263#418—71no—
264#413—71no—
265#410—71no—
266C23×C7—21no—
267C23×C7C2×C3×D411yescharacteristic
268C22×D7—22no—
269C22×D7—28no—
270C22×D7—22no—
271C22×D7—22no—
272C22×D7—82no—
273C22×D7—84no—
274C22×D7C3×C22⋊C412yes—
275C7×Q8—21no—
276C7×Q8C3×C22⋊C412yes—
277C7×D4—22no—
278C7×D4—22no—
279C7×D4—21no—
280C7×D4C3×C22⋊C412yes—
281C2×C4×C7—21no—
282C2×C4×C7—22no—
283C2×C4×C7—22no—
284C2×C4×C7—41no—
285C2×C4×C7C22×C3×C411yescharacteristic
286C2×C4×C7C2×C3×D411yescharacteristic
287C2×C4×C7C2×C3×D411yescharacteristic
288C2×C4×C7C2×C3×D411yescharacteristic
289C2×C4×C7C2×C3×D411yescharacteristic
290C2×C4×C7C2×C3×D411yescharacteristic
291C22⋊D7—28no—
292C22⋊D7—22no—
293C22⋊D7—22no—
294C2×Dic7—41no—
295C2×Dic7C3×C22⋊C412yes—
296D28—28no—
297D28—22no—
298D28—21no—
299D28—22no—
300D28—21no—
301D28—22no—
302D28C3×C22⋊C414yes—
303C4×D7—28no—
304C4×D7—22no—
305C4×D7—22no—
306Dic14—21no—
307Dic14—21no—
308C7×C8—41no—
309C7⋊C8—41no—
310C24×C3—142no—
311C24×C3—141no—
312C3×#41—72no—
313C3×#41—72no—
314C3×#41—141no—
315C3×#41—141no—
316C3×#41—141no—
317C3×#41—141no—
318C3×#41—141no—
319C3×#41—141no—
320C3×#41—144no—
321C3×#41—144no—
322C3×#41—144no—
323C3×#41—144no—
324C2×C3×Q8—71no—
325C2×C3×Q8—71no—
326C2×C3×D4—72no—
327C2×C3×D4—72no—
328C2×C3×D4—72no—
329C2×C3×D4—72no—
330C2×C3×D4—71no—
331C2×C3×D4—71no—
332C2×C3×D4—141no—
333C2×C3×D4—141no—
334C2×C3×D4—141no—
335C2×C3×D4—141no—
336C2×C3×D4—142no—
337C2×C3×D4—144no—
338C2×C3×D4—144no—
339C2×C3×D4—142no—
340C2×C3×D4—144no—
341C2×C3×D4—144no—
342C2×C3×D4—148no—
343C2×C3×D4—148no—
344C22×C3×C4—72no—
345C22×C3×C4—71no—
346C22×C3×C4—141no—
347C22×C3×C4—142no—
348C3×M16—141no—
349C3×M16—141no—
350C3×M16—141no—
351C3×M16—141no—
352C2×C3×C8—141no—
353C2×C3×C8—141no—
354C3×C4⋊C4—141no—
355C3×C4⋊C4—141no—
356C3×C22⋊C4—141no—
357C3×C22⋊C4—141no—
358C3×C42—141no—
359C3×C42—141no—
360C2×ΓL(1,𝔽8)—21no—
361C2×ΓL(1,𝔽8)—21no—
362C2×ΓL(1,𝔽8)—21no—
363C2×ΓL(1,𝔽8)—42no—
364C2×ΓL(1,𝔽8)#37911yescharacteristic
365AGL(1,𝔽7)—44no—
366AGL(1,𝔽7)—42no—
367H(5,𝔽2)—142no—
368H(5,𝔽2)—142no—
369H(5,𝔽2)—142no—
370H(5,𝔽2)—142no—
371C2×#41—71no—
372C2×#41—72no—
373C2×#41—141no—
374C2×#41C2×AGL(1,𝔽7)11yescharacteristic
375C22×D4—72no—
376C22×D4—71no—
377C22×D4—141no—
378C22×D4—142no—
379C2×M16—71no—
380C2×M16C2×AGL(1,𝔽7)11yescharacteristic, complemented
381#117—71no—
382#117C2×AGL(1,𝔽7)11yescharacteristic, complemented
383#104—22no—
384#104—142no—
385#102—142no—
386#102—142no—
387#101—141no—
388#100—141no—
389#99—142no—
390C22×C7—22no—
391C22×C7—41no—
392C22×C7—42no—
393C22×C7C2×C3×C22⋊C411yescharacteristic
394C22×C7C3×#12011yescharacteristic
395C22×C7C3×#12011yescharacteristic
396C2×D7—22no—
397C2×D7—24no—
398C2×D7—44no—
399C2×D7—42no—
400C2×D7—82no—
401C2×D7—82no—
402C2×D7—88no—
403C4×C7—22no—
404C4×C7—81no—
405C4×C7C2×C3×C22⋊C411yescharacteristic
406C4×C7C2×C3×C22⋊C411yescharacteristic
407C4×C7C3×#12011yescharacteristic
408C4×C7C3×#12011yescharacteristic
409Dic7—22no—
410Dic7—81no—
411C23×C3—72no—
412C23×C3—71no—
413C23×C3—141no—
414C23×C3—142no—
415C23×C3—142no—
416C23×C3—142no—
417C23×C3—148no—
418C23×C3—562no—
419C23×C3—564no—
420C3×Q8—72no—
421C3×Q8—141no—
422C3×Q8—141no—
423C3×Q8—141no—
424C3×D4—74no—
425C3×D4—72no—
426C3×D4—141no—
427C3×D4—142no—
428C3×D4—142no—
429C3×D4—142no—
430C3×D4—141no—
431C3×D4—142no—
432C3×D4—142no—
433C3×D4—141no—
434C3×D4—142no—
435C3×D4—142no—
436C3×D4—148no—
437C3×D4—148no—
438C2×C3×C4—72no—
439C2×C3×C4—71no—
440C2×C3×C4—71no—
441C2×C3×C4—71no—
442C2×C3×C4—71no—
443C2×C3×C4—71no—
444C2×C3×C4—71no—
445C2×C3×C4—142no—
446C2×C3×C4—142no—
447C2×C3×C4—141no—
448C2×C3×C4—142no—
449C2×C3×C4—142no—
450C2×C3×C4—148no—
451C2×C3×C4—281no—
452C2×C3×C4—281no—
453C3×C8—281no—
454C3×C8—281no—
455ΓL(1,𝔽8)#179511yescharacteristic, complemented, Hall
456C24—142no—
457C24—141no—
458#41—21no—
459#41—21no—
460#41—144no—
461#41—144no—
462#41—144no—
463#41—144no—
464#41—141no—
465#41—141no—
466#41—141no—
467#41—141no—
468#41C4⋊AGL(1,𝔽7)12yes—
469#41(C22⋊D7)⋊C312yes—
470C2×Q8—71no—
471C2×Q8C4×AGL(1,𝔽7)11yescharacteristic
472C2×D4—21no—
473C2×D4—72no—
474C2×D4—72no—
475C2×D4—72no—
476C2×D4—72no—
477C2×D4—71no—
478C2×D4—142no—
479C2×D4—144no—
480C2×D4—144no—
481C2×D4—142no—
482C2×D4—144no—
483C2×D4—148no—
484C2×D4—148no—
485C2×D4—144no—
486C2×D4—141no—
487C2×D4—141no—
488C2×D4—141no—
489C2×D4C4×AGL(1,𝔽7)11yescharacteristic
490C22×C4—21no—
491C22×C4—72no—
492C22×C4—142no—
493C22×C4C22×AGL(1,𝔽7)11yescharacteristic
494M16—21no—
495M16—21no—
496M16—141no—
497M16—141no—
498C2×C8—21no—
499C2×C8—141no—
500C4⋊C4—21no—
501C4⋊C4—141no—
502C22⋊C4—21no—
503C22⋊C4—141no—
504C42—21no—
505C42—141no—
506C2×C7—21no—
507C2×C7—21no—
508C2×C7—21no—
509C2×C7—42no—
510C2×C7C3×#37911yescharacteristic
511D7—44no—
512D7—42no—
513C22×C3—71no—
514C22×C3—71no—
515C22×C3—71no—
516C22×C3—142no—
517C22×C3—144no—
518C22×C3—142no—
519C22×C3—281no—
520C22×C3—282no—
521C22×C3—282no—
522C22×C3—284no—
523C22×C3—562no—
524C22×C3—562no—
525C22×C3—568no—
526C3×C4—71no—
527C3×C4—71no—
528C3×C4—71no—
529C3×C4—71no—
530C3×C4—142no—
531C3×C4—142no—
532C3×C4—561no—
533C3×C4—561no—
534C23—21no—
535C23—72no—
536C23—148no—
537C23—142no—
538C23—142no—
539C23—142no—
540C23—562no—
541C23—564no—
542C23D4×AGL(1,𝔽7)11yescharacteristic
543Q8—21no—
544Q8—141no—
545Q8—141no—
546Q8(C2×AGL(1,𝔽7))⋊C412yes—
547D4—22no—
548D4—22no—
549D4—21no—
550D4—74no—
551D4—148no—
552D4—148no—
553D4—142no—
554D4—142no—
555D4—142no—
556D4—141no—
557D4—142no—
558D4—142no—
559D4—141no—
560D4(C2×AGL(1,𝔽7))⋊C412yes—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—41no—
565C2×C4—72no—
566C2×C4—148no—
567C2×C4—142no—
568C2×C4—142no—
569C2×C4—281no—
570C2×C4C2×C4×AGL(1,𝔽7)11yescharacteristic
571C2×C4C2×C4⋊AGL(1,𝔽7)11yescharacteristic
572C2×C4D4×AGL(1,𝔽7)11yescharacteristic
573C2×C4D4×AGL(1,𝔽7)11yescharacteristic
574C2×C4D4×AGL(1,𝔽7)11yescharacteristic
575C2×C4C2×(C22⋊D7)⋊C311yescharacteristic
576C8—41no—
577C8—281no—
578C7C3×#179511yescharacteristic, complemented, Sylow
579C2×C3—71no—
580C2×C3—141no—
581C2×C3—141no—
582C2×C3—141no—
583C2×C3—282no—
584C2×C3—284no—
585C2×C3—282no—
586C22—22no—
587C22—41no—
588C22—42no—
589C22—144no—
590C22—142no—
591C22—282no—
592C22—284no—
593C22—562no—
594C22—562no—
595C22—568no—
596C22C22⋊C4×AGL(1,𝔽7)11yescharacteristic
597C22#6445⋊C311yescharacteristic
598C22#6500⋊C311yescharacteristic
599C4—22no—
600C4—81no—
601C4—142no—
602C4—561no—
603C4C22⋊C4×AGL(1,𝔽7)11yescharacteristic
604C4#6445⋊C311yescharacteristic
605C4C2×(C2×AGL(1,𝔽7))⋊C411yescharacteristic
606C4#6500⋊C311yescharacteristic
607C3—71noSylow
608C2—21no—
609C2—21no—
610C2—21no—
611C2—42no—
612C2—284no—
613C2—282no—
614C2#89727⋊C311yescharacteristic
subgroupG/H
centerC2#89727⋊C3
commutatorC2×C4×C7C22×C3×C4
FrattiniC22×C4C22×AGL(1,𝔽7)
FittingC7×#421C2×C3
socleC2×C7C3×#379
prime radicalC2×#10621518C2
cosocleC22×C4×C7C23×C3
hypercenter#421AGL(1,𝔽7)
hypocenterC7C3×#1795
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. ΓL(1,𝔽8)×#421C2semidirect
3. #90008⋊C3C2semidirect
4. #89904⋊C3C2semidirect
5. #89903⋊C3C2semidirect
6. #89778⋊C3C2semidirect
7. #89773⋊C3C2semidirect
8. #11728168C3semidirect
14. C2×#66659C4semidirect
16. C2×D4×AGL(1,𝔽7)C4semidirect
21. C2×M16×ΓL(1,𝔽8)C22semidirect
22. ΓL(1,𝔽8)×#117C22semidirect
23. #6489⋊C3C22semidirect
24. C2×#1136⋊C3C22semidirect
33. C7×#421C2×C3semidirect
34. #90008C2×C3semidirect
35. #89904C2×C3semidirect
36. #89903C2×C3semidirect
37. #89778C2×C3semidirect
38. #89773C2×C3semidirect
95. C2×#1161C3×C4semidirect
97. C2×D4×D7C3×C4semidirect
102. C2×C7×M16C22×C3semidirect
103. C7×#117C22×C3semidirect
104. #6489C22×C3semidirect
105. C2×#1136C22×C3semidirect
261. #421AGL(1,𝔽7)semidirect
380. C2×M16C2×AGL(1,𝔽7)semidirect
382. #117C2×AGL(1,𝔽7)semidirect
455. ΓL(1,𝔽8)#1795semidirect
578. C7C3×#1795semidirect

Maximal subgroups

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

subgroupindex
C2×#106215182
ΓL(1,𝔽8)×#4212
#90008⋊C32
#89904⋊C32
#89903⋊C32
#89778⋊C32
#89773⋊C32
#117281683
C3×#17957