Finite Group Databasebeta

← #72277620

Subgroups — #72277620

Order 2688.

1532 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13062154C211yesmaximal, characteristic, complemented
2ΓL(1,𝔽8)×#525C211yesmaximal, characteristic, complemented
3#90482⋊C3C212yesmaximal, complemented
4#90012⋊C3C211yesmaximal, characteristic, complemented
5#89825⋊C3C214yesmaximal, complemented
6#89804⋊C3C214yesmaximal, complemented
7#89778⋊C3C212yesmaximal, complemented
8#11740381C311yesmaximal, characteristic, complemented, Hall
9C2×#41×ΓL(1,𝔽8)C2211yescharacteristic
10C23×C4×ΓL(1,𝔽8)C2211yescharacteristic, complemented
11#10621519—22no—
12#10621518—22no—
13#41×AGL(1,𝔽7)—24no—
14#10621516—21no—
15#6548⋊C3—21no—
16#6548⋊C3C2214yes—
17C2×#1157⋊C3—22no—
18C2×#1157⋊C3C2212yes—
19ΓL(1,𝔽8)×#123C2212yescomplemented
20ΓL(1,𝔽8)×C22⋊Q8—21no—
21ΓL(1,𝔽8)×#121—21no—
22ΓL(1,𝔽8)×#120C2212yescomplemented
23C4×D4×ΓL(1,𝔽8)—22no—
24ΓL(1,𝔽8)×#117C2211yescharacteristic, complemented
25#10620789C2214yescomplemented
26#6493⋊C3—22no—
27#6492⋊C3C2214yescomplemented
28C4×(C22⋊D7)⋊C3—24no—
29#6489⋊C3C2212yescomplemented
30#6487⋊C3—22no—
31#6408⋊C3C2214yescomplemented
32#6380⋊C3C2218yescomplemented
33#90616C2×C311yescharacteristic, complemented
34C7×#525C2×C311yescharacteristic, complemented
35#90482C2×C312yescomplemented
36#90012C2×C311yescharacteristic, complemented
37#89825C2×C314yescomplemented
38#89804C2×C314yescomplemented
39#89778C2×C312yescomplemented
40C3×#3025—71nomaximal, Hall
41C24×ΓL(1,𝔽8)C2311yescharacteristic
42#41×ΓL(1,𝔽8)—22no—
43#41×ΓL(1,𝔽8)—22no—
44C2×Q8×ΓL(1,𝔽8)D411yescharacteristic, complemented
45C2×D4×ΓL(1,𝔽8)—22no—
46C2×D4×ΓL(1,𝔽8)D411yescharacteristic, complemented
47C2×D4×ΓL(1,𝔽8)C2312yes—
48C22×C4×ΓL(1,𝔽8)—22no—
49C22×C4×ΓL(1,𝔽8)—22no—
50C22×C4×ΓL(1,𝔽8)—21no—
51C22×C4×ΓL(1,𝔽8)—21no—
52C22×C4×ΓL(1,𝔽8)D412yescomplemented
53C22×C4×ΓL(1,𝔽8)C2311yescharacteristic
54C22×C4×ΓL(1,𝔽8)C2311yescharacteristic
55C2×(C22⋊D7)⋊C3—24no—
56C2×(C22⋊D7)⋊C3—24no—
57C2×(C22⋊D7)⋊C3C2314yes—
58#66659—24no—
59Q8×AGL(1,𝔽7)—24no—
60#1159⋊C3—24no—
61#1159⋊C3—28no—
62D4×AGL(1,𝔽7)—24no—
63D4×AGL(1,𝔽7)—28no—
64#1157⋊C3—24no—
65#1157⋊C3—24no—
66#1157⋊C3—22no—
67#1157⋊C3—24no—
68#1157⋊C3—22no—
69#1157⋊C3—22no—
70#1157⋊C3—22no—
71C2×C4⋊AGL(1,𝔽7)—22no—
72C2×C4⋊AGL(1,𝔽7)D412yescomplemented
73C2×C4×AGL(1,𝔽7)—24no—
74C2×C4×AGL(1,𝔽7)D414yescomplemented
75C2×ΓL(1,𝔽8)⋊Q8—22no—
76C2×ΓL(1,𝔽8)⋊Q8D412yescomplemented
77C4⋊C4×ΓL(1,𝔽8)—21no—
78C4⋊C4×ΓL(1,𝔽8)—22no—
79C22⋊C4×ΓL(1,𝔽8)—22no—
80C22⋊C4×ΓL(1,𝔽8)—22no—
81C22⋊C4×ΓL(1,𝔽8)C2312yes—
82C42×ΓL(1,𝔽8)—21no—
83(C22⋊Dic7)⋊C3—24no—
84(C22⋊Dic7)⋊C3C2314yes—
85(C2×AGL(1,𝔽7))⋊C4—24no—
86C4⋊(ΓL(1,𝔽8)⋊C4)—22no—
87(ΓL(1,𝔽8)⋊C4)⋊C4—24no—
88C4×ΓL(1,𝔽8)⋊C4—22no—
89C2×C7×#41C22×C311yescharacteristic
90C23×C4×C7C22×C311yescharacteristic, complemented
91#6554—22no—
92#6553—22no—
93D7×#41—24no—
94#6551—21no—
95#6548—21no—
96#6548C22×C314yes—
97C2×#1157—22no—
98C2×#1157C22×C312yes—
99C7×#123C22×C312yescomplemented
100C7×C22⋊Q8—21no—
101C7×#121—21no—
102C7×#120C22×C312yescomplemented
103C4×C7×D4—22no—
104C7×#117C22×C311yescharacteristic, complemented
105#6516C22×C314yescomplemented
106#6493—22no—
107#6492C22×C314yescomplemented
108C4×C22⋊D7—24no—
109#6489C22×C312yescomplemented
110#6487—22no—
111#6408C22×C314yescomplemented
112#6380C22×C318yescomplemented
113C3×#585—71no—
114C3×#525—72no—
115C3×#525—71no—
116C3×#458—74no—
117C3×B(4,𝔽2)—74no—
118C3×#410—71no—
119C3×#410—72no—
120C23×ΓL(1,𝔽8)—21no—
121C23×ΓL(1,𝔽8)—22no—
122C23×ΓL(1,𝔽8)—42no—
123C23×ΓL(1,𝔽8)C2×D412yes—
124C23×ΓL(1,𝔽8)C2411yescharacteristic
125C22×AGL(1,𝔽7)—24no—
126C22×AGL(1,𝔽7)C2×D414yes—
127Q8×ΓL(1,𝔽8)—22no—
128D4×ΓL(1,𝔽8)—24no—
129D4×ΓL(1,𝔽8)—22no—
130D4×ΓL(1,𝔽8)—44no—
131C2×C4×ΓL(1,𝔽8)—22no—
132C2×C4×ΓL(1,𝔽8)—22no—
133C2×C4×ΓL(1,𝔽8)—22no—
134C2×C4×ΓL(1,𝔽8)—21no—
135C2×C4×ΓL(1,𝔽8)—22no—
136C2×C4×ΓL(1,𝔽8)—41no—
137C2×C4×ΓL(1,𝔽8)—42no—
138C2×C4×ΓL(1,𝔽8)—41no—
139C2×C4×ΓL(1,𝔽8)C2×D412yes—
140C2×C4×ΓL(1,𝔽8)C2×D411yescharacteristic
141C2×C4×ΓL(1,𝔽8)C2×D411yescharacteristic
142C2×C4×ΓL(1,𝔽8)C2×D412yes—
143C2×C4×ΓL(1,𝔽8)C2×D412yes—
144(C22⋊D7)⋊C3—28no—
145(C22⋊D7)⋊C3—24no—
146(C22⋊D7)⋊C3—24no—
147(C22⋊D7)⋊C3—48no—
148C2×ΓL(1,𝔽8)⋊C4—24no—
149C2×ΓL(1,𝔽8)⋊C4—24no—
150C2×ΓL(1,𝔽8)⋊C4C2×D414yes—
151C4⋊AGL(1,𝔽7)—24no—
152C4⋊AGL(1,𝔽7)—22no—
153C4⋊AGL(1,𝔽7)—22no—
154C4×AGL(1,𝔽7)—28no—
155C4×AGL(1,𝔽7)—24no—
156C4×AGL(1,𝔽7)—24no—
157ΓL(1,𝔽8)⋊Q8—24no—
158ΓL(1,𝔽8)⋊Q8—22no—
159ΓL(1,𝔽8)⋊Q8—22no—
160#3025—71noSylow
161C24×C7C23×C311yescharacteristic
162C7×#41—22no—
163C7×#41—22no—
164C2×C7×Q8C3×D411yescharacteristic, complemented
165C2×C7×D4—22no—
166C2×C7×D4C3×D411yescharacteristic, complemented
167C2×C7×D4C23×C312yes—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7C3×D412yescomplemented
173C22×C4×C7C23×C311yescharacteristic
174C22×C4×C7C23×C311yescharacteristic
175C2×C22⋊D7—24no—
176C2×C22⋊D7—24no—
177C2×C22⋊D7C23×C314yes—
178#1161—24no—
179Q8×D7—24no—
180#1159—24no—
181#1159—28no—
182D4×D7—24no—
183D4×D7—28no—
184#1157—24no—
185#1157—24no—
186#1157—22no—
187#1157—24no—
188#1157—22no—
189#1157—22no—
190#1157—22no—
191C2×D28—22no—
192C2×D28C3×D412yescomplemented
193C2×C4×D7—24no—
194C2×C4×D7C3×D414yescomplemented
195C2×Dic14—22no—
196C2×Dic14C3×D412yescomplemented
197C7×C4⋊C4—21no—
198C7×C4⋊C4—22no—
199C7×C22⋊C4—22no—
200C7×C22⋊C4—22no—
201C7×C22⋊C4C23×C312yes—
202C42×C7—21no—
203C22⋊Dic7—24no—
204C22⋊Dic7C23×C314yes—
205(C2×D7)⋊C4—24no—
206C4⋊Dic7—22no—
207Dic7⋊C4—24no—
208C4×Dic7—22no—
209C3×2−1+4—141no—
210C3×2−1+4—142no—
211C3×H(5,𝔽2)—74no—
212C3×H(5,𝔽2)—141no—
213C3×H(5,𝔽2)—142no—
214C2×C3×#41—72no—
215C2×C3×#41—71no—
216C2×C3×#41—142no—
217C2×C3×#41—144no—
218C23×C3×C4—71no—
219C3×#123—74no—
220C3×#123—72no—
221C3×C22⋊Q8—141no—
222C3×C22⋊Q8—142no—
223C3×#121—141no—
224C3×#121—142no—
225C3×#120—74no—
226C3×#120—72no—
227C3×C4×D4—142no—
228C3×C4×D4—144no—
229C3×#117—72no—
230C3×#117—71no—
231C3×#99—78no—
232C3×#99—74no—
233C22×ΓL(1,𝔽8)—24no—
234C22×ΓL(1,𝔽8)—22no—
235C22×ΓL(1,𝔽8)—22no—
236C22×ΓL(1,𝔽8)—41no—
237C22×ΓL(1,𝔽8)—42no—
238C22×ΓL(1,𝔽8)—42no—
239C22×ΓL(1,𝔽8)—41no—
240C22×ΓL(1,𝔽8)—41no—
241C22×ΓL(1,𝔽8)C22×D412yes—
242C22×ΓL(1,𝔽8)C22×D411yescharacteristic
243C2×AGL(1,𝔽7)—24no—
244C2×AGL(1,𝔽7)—44no—
245C2×AGL(1,𝔽7)—84no—
246C4×ΓL(1,𝔽8)—22no—
247C4×ΓL(1,𝔽8)—42no—
248C4×ΓL(1,𝔽8)—41no—
249C4×ΓL(1,𝔽8)#12011yescharacteristic
250C4×ΓL(1,𝔽8)#12012yes—
251C4×ΓL(1,𝔽8)#12011yescharacteristic
252ΓL(1,𝔽8)⋊C4—24no—
253ΓL(1,𝔽8)⋊C4—44no—
254#585—71no—
255#525—72no—
256#525AGL(1,𝔽7)11yescharacteristic, complemented
257#458—74no—
258B(4,𝔽2)—74no—
259#410—71no—
260#410—72no—
261C23×C7—22no—
262C23×C7—21no—
263C23×C7—42no—
264C23×C7C2×C3×D412yes—
265C23×C7C24×C311yescharacteristic
266C22×D7—24no—
267C22×D7C2×C3×D414yes—
268C7×Q8—22no—
269C7×D4—24no—
270C7×D4—22no—
271C7×D4—44no—
272C2×C4×C7—22no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—21no—
277C2×C4×C7—41no—
278C2×C4×C7—42no—
279C2×C4×C7—41no—
280C2×C4×C7C2×C3×D412yes—
281C2×C4×C7C2×C3×D412yes—
282C2×C4×C7C2×C3×D412yes—
283C2×C4×C7C2×C3×D411yescharacteristic
284C2×C4×C7C2×C3×D411yescharacteristic
285C22⋊D7—28no—
286C22⋊D7—24no—
287C22⋊D7—24no—
288C22⋊D7—48no—
289C2×Dic7—24no—
290C2×Dic7—24no—
291C2×Dic7C2×C3×D414yes—
292D28—24no—
293D28—22no—
294D28—22no—
295C4×D7—28no—
296C4×D7—24no—
297C4×D7—24no—
298Dic14—24no—
299Dic14—22no—
300Dic14—22no—
301C24×C3—71no—
302C3×#41—142no—
303C3×#41—142no—
304C3×#41—142no—
305C3×#41—142no—
306C3×#41—142no—
307C3×#41—142no—
308C3×#41—144no—
309C3×#41—148no—
310C3×#41—144no—
311C3×#41—144no—
312C3×#41—144no—
313C3×#41—144no—
314C2×C3×Q8—72no—
315C2×C3×Q8—71no—
316C2×C3×Q8—142no—
317C2×C3×Q8—144no—
318C2×C3×D4—74no—
319C2×C3×D4—72no—
320C2×C3×D4—71no—
321C2×C3×D4—72no—
322C2×C3×D4—142no—
323C2×C3×D4—148no—
324C2×C3×D4—144no—
325C2×C3×D4—142no—
326C2×C3×D4—144no—
327C2×C3×D4—144no—
328C22×C3×C4—74no—
329C22×C3×C4—72no—
330C22×C3×C4—71no—
331C22×C3×C4—71no—
332C22×C3×C4—142no—
333C22×C3×C4—141no—
334C22×C3×C4—142no—
335C22×C3×C4—141no—
336C22×C3×C4—144no—
337C3×C4⋊C4—141no—
338C3×C4⋊C4—142no—
339C3×C4⋊C4—142no—
340C3×C4⋊C4—144no—
341C3×C22⋊C4—74no—
342C3×C22⋊C4—72no—
343C3×C22⋊C4—142no—
344C3×C22⋊C4—142no—
345C3×C22⋊C4—144no—
346C3×C22⋊C4—144no—
347C3×C42—141no—
348C3×C42—142no—
349C2×ΓL(1,𝔽8)—22no—
350C2×ΓL(1,𝔽8)—21no—
351C2×ΓL(1,𝔽8)—42no—
352C2×ΓL(1,𝔽8)—42no—
353C2×ΓL(1,𝔽8)C2×#12011yescharacteristic
354AGL(1,𝔽7)—44no—
3552−1+4—142no—
3562−1+4—141no—
357H(5,𝔽2)—74no—
358H(5,𝔽2)—142no—
359H(5,𝔽2)—141no—
360C2×#41—72no—
361C2×#41—144no—
362C2×#41—142no—
363C2×#41C2×AGL(1,𝔽7)11yescharacteristic
364C23×C4C2×AGL(1,𝔽7)11yescharacteristic, complemented
365#123—74no—
366#123C2×AGL(1,𝔽7)12yescomplemented
367C22⋊Q8—21no—
368C22⋊Q8—142no—
369#121—21no—
370#121—142no—
371#120—74no—
372#120C2×AGL(1,𝔽7)12yescomplemented
373C4×D4—22no—
374C4×D4—144no—
375#117—72no—
376#117C2×AGL(1,𝔽7)11yescharacteristic, complemented
377#99—74no—
378#99—78no—
379C22×C7—24no—
380C22×C7—22no—
381C22×C7—22no—
382C22×C7—41no—
383C22×C7—42no—
384C22×C7—42no—
385C22×C7—41no—
386C22×C7—41no—
387C22×C7C22×C3×D412yes—
388C22×C7C22×C3×D411yescharacteristic
389C2×D7—24no—
390C2×D7—44no—
391C2×D7—84no—
392C4×C7—22no—
393C4×C7—42no—
394C4×C7—41no—
395C4×C7C3×#12011yescharacteristic
396C4×C7C3×#12012yes—
397C4×C7C3×#12011yescharacteristic
398Dic7—24no—
399Dic7—44no—
400C23×C3—74no—
401C23×C3—72no—
402C23×C3—71no—
403C23×C3—142no—
404C23×C3—141no—
405C23×C3—144no—
406C23×C3—282no—
407C3×Q8—142no—
408C3×Q8—142no—
409C3×Q8—142no—
410C3×Q8—144no—
411C3×D4—142no—
412C3×D4—144no—
413C3×D4—142no—
414C3×D4—142no—
415C3×D4—144no—
416C3×D4—144no—
417C3×D4—144no—
418C3×D4—148no—
419C3×D4—284no—
420C3×D4—288no—
421C2×C3×C4—74no—
422C2×C3×C4—72no—
423C2×C3×C4—72no—
424C2×C3×C4—71no—
425C2×C3×C4—71no—
426C2×C3×C4—72no—
427C2×C3×C4—142no—
428C2×C3×C4—142no—
429C2×C3×C4—142no—
430C2×C3×C4—142no—
431C2×C3×C4—141no—
432C2×C3×C4—144no—
433C2×C3×C4—144no—
434C2×C3×C4—148no—
435C2×C3×C4—144no—
436C2×C3×C4—144no—
437C2×C3×C4—281no—
438C2×C3×C4—282no—
439C2×C3×C4—281no—
440ΓL(1,𝔽8)#302511yescharacteristic, complemented, Hall
441C24C22×AGL(1,𝔽7)11yescharacteristic
442#41—22no—
443#41—22no—
444#41—144no—
445#41—144no—
446#41—148no—
447#41—144no—
448#41—144no—
449#41—142no—
450#41—142no—
451#41—142no—
452#41—142no—
453#41—144no—
454C2×Q8—72no—
455C2×Q8—142no—
456C2×Q8—144no—
457C2×Q8(C22⋊D7)⋊C311yescharacteristic, complemented
458C2×D4—22no—
459C2×D4—74no—
460C2×D4—72no—
461C2×D4—142no—
462C2×D4—148no—
463C2×D4—144no—
464C2×D4—144no—
465C2×D4—144no—
466C2×D4(C22⋊D7)⋊C311yescharacteristic, complemented
467C2×D4C22×AGL(1,𝔽7)12yes—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—74no—
473C22×C4—144no—
474C22×C4(C22⋊D7)⋊C312yescomplemented
475C22×C4C22×AGL(1,𝔽7)11yescharacteristic
476C22×C4C22×AGL(1,𝔽7)11yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—22no—
479C4⋊C4—144no—
480C4⋊C4—142no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—74no—
484C22⋊C4—144no—
485C22⋊C4—144no—
486C22⋊C4C22×AGL(1,𝔽7)12yes—
487C42—21no—
488C42—142no—
489C2×C7—22no—
490C2×C7—21no—
491C2×C7—42no—
492C2×C7—42no—
493C2×C7C2×C3×#12011yescharacteristic
494D7—44no—
495C22×C3—72no—
496C22×C3—71no—
497C22×C3—142no—
498C22×C3—142no—
499C22×C3—144no—
500C22×C3—144no—
501C22×C3—281no—
502C22×C3—281no—
503C22×C3—282no—
504C22×C3—281no—
505C22×C3—282no—
506C22×C3—284no—
507C22×C3—564no—
508C3×C4—71no—
509C3×C4—72no—
510C3×C4—71no—
511C3×C4—142no—
512C3×C4—144no—
513C3×C4—281no—
514C3×C4—282no—
515C3×C4—284no—
516C23—22no—
517C23—21no—
518C23—42no—
519C23—74no—
520C23—144no—
521C23C2×(C22⋊D7)⋊C312yes—
522C23C23×AGL(1,𝔽7)11yescharacteristic
523Q8—22no—
524Q8—144no—
525Q8—142no—
526Q8—142no—
527D4—24no—
528D4—22no—
529D4—44no—
530D4—144no—
531D4—148no—
532D4—144no—
533D4—144no—
534D4—142no—
535D4—142no—
536D4—288no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—74no—
546C2×C4—148no—
547C2×C4—144no—
548C2×C4—144no—
549C2×C4—144no—
550C2×C4—144no—
551C2×C4D4×AGL(1,𝔽7)12yes—
552C2×C4D4×AGL(1,𝔽7)12yes—
553C2×C4C2×(C22⋊D7)⋊C312yes—
554C2×C4C2×(C22⋊D7)⋊C311yescharacteristic
555C2×C4C2×(C22⋊D7)⋊C311yescharacteristic
556C7C3×#302511yescharacteristic, complemented, Sylow
557C2×C3—71no—
558C2×C3—141no—
559C2×C3—142no—
560C2×C3—282no—
561C2×C3—282no—
562C2×C3—284no—
563C22—22no—
564C22—24no—
565C22—22no—
566C22—41no—
567C22—42no—
568C22—41no—
569C22—42no—
570C22—41no—
571C22—144no—
572C22—284no—
573C22—564no—
574C22C2×D4×AGL(1,𝔽7)12yes—
575C22C22×(C22⋊D7)⋊C311yescharacteristic
576C4—22no—
577C4—42no—
578C4—41no—
579C4—144no—
580C4—284no—
581C4#6500⋊C311yescharacteristic
582C4#6500⋊C312yes—
583C4#6500⋊C311yescharacteristic
584C3—71noSylow
585C2—21no—
586C2—22no—
587C2—42no—
588C2—42no—
589C2—284no—
590C2C2×#6500⋊C311yescharacteristic
subgroupG/H
centerC4#6500⋊C3
commutator, cosocleC23×C7C24×C3
FrattiniC23C23×AGL(1,𝔽7)
FittingC7×#525C2×C3
socleC2×C7C2×C3×#120
hypercenter#525AGL(1,𝔽7)
hypocenterC7C3×#3025
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #13062154C2semidirect
2. ΓL(1,𝔽8)×#525C2semidirect
3. #90482⋊C3C2semidirect
4. #90012⋊C3C2semidirect
5. #89825⋊C3C2semidirect
6. #89804⋊C3C2semidirect
7. #89778⋊C3C2semidirect
8. #11740381C3semidirect
10. C23×C4×ΓL(1,𝔽8)C22semidirect
19. ΓL(1,𝔽8)×#123C22semidirect
22. ΓL(1,𝔽8)×#120C22semidirect
24. ΓL(1,𝔽8)×#117C22semidirect
25. #10620789C22semidirect
27. #6492⋊C3C22semidirect
29. #6489⋊C3C22semidirect
31. #6408⋊C3C22semidirect
32. #6380⋊C3C22semidirect
33. #90616C2×C3semidirect
34. C7×#525C2×C3semidirect
35. #90482C2×C3semidirect
36. #90012C2×C3semidirect
37. #89825C2×C3semidirect
38. #89804C2×C3semidirect
39. #89778C2×C3semidirect
44. C2×Q8×ΓL(1,𝔽8)D4semidirect
46. C2×D4×ΓL(1,𝔽8)D4semidirect
52. C22×C4×ΓL(1,𝔽8)D4semidirect
72. C2×C4⋊AGL(1,𝔽7)D4semidirect
74. C2×C4×AGL(1,𝔽7)D4semidirect
76. C2×ΓL(1,𝔽8)⋊Q8D4semidirect
90. C23×C4×C7C22×C3semidirect
99. C7×#123C22×C3semidirect
102. C7×#120C22×C3semidirect
104. C7×#117C22×C3semidirect
105. #6516C22×C3semidirect
107. #6492C22×C3semidirect
109. #6489C22×C3semidirect
111. #6408C22×C3semidirect
112. #6380C22×C3semidirect
164. C2×C7×Q8C3×D4semidirect
166. C2×C7×D4C3×D4semidirect
172. C22×C4×C7C3×D4semidirect
192. C2×D28C3×D4semidirect
194. C2×C4×D7C3×D4semidirect
196. C2×Dic14C3×D4semidirect
256. #525AGL(1,𝔽7)semidirect
364. C23×C4C2×AGL(1,𝔽7)semidirect
366. #123C2×AGL(1,𝔽7)semidirect
372. #120C2×AGL(1,𝔽7)semidirect
376. #117C2×AGL(1,𝔽7)semidirect
440. ΓL(1,𝔽8)#3025semidirect
457. C2×Q8(C22⋊D7)⋊C3semidirect
466. C2×D4(C22⋊D7)⋊C3semidirect
474. C22×C4(C22⋊D7)⋊C3semidirect
556. C7C3×#3025semidirect

Maximal subgroups

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

subgroupindex
#130621542
ΓL(1,𝔽8)×#5252
#90482⋊C32
#90012⋊C32
#89825⋊C32
#89804⋊C32
#89778⋊C32
#117403813
C3×#30257